Obviously if you're going to spray sulfuric acid everywhere, you'd want full PPE. And not to mistake it for water. 
Truthfully, that sort of thing could have happened to me in my full-on mad scientist phase last year. I'd run out of glassware and end up using drinking cups from time to time.
Then again, though, it's not possible to drink a strong acid and not immediately detect the extremely sour flavor and try to spit it out. Daddy might get part of a mouthful before spitting it out and realizing with horror what he'd done, and then try to rinse his mouth out as it corroded. The result would be severe burns and tissue damage throughout the mouth and lips but probably nothing fatal. If some were swallowed it would cause severe damage to the esophagus and possibly stomach, but still survivable with modern medicine.
It's pretty hard to die of acid or base exposure, even to the mouth, but very easy to be permanently maimed. That's why they are so popular among revenge-seeking jilted ex-lovers and the like - the attack maims the victim but rarely kills her. In a way, the goal is to be crueler than murder - to leave them alive, but severely disfigured and suffering for the rest of their lives.
I've licked up little droplets of straight phosphoric acid (weaker than H2SO4 or HCl, but still strong enough to be corrosive), fairly concentrated sodium bisulfate (similar to phosphoric in strength - it's a half-neutralized version of H2SO4), and relatively dilute HCl. All are intensely sour and HCl in particular has the same acidic taste as vomit - mostly because stomach acid is HCl.
Here's my overall review of the acids I've played with at home, ranked by how much I liked using them. I'll also include a couple of acids I've not played with in brackets, with my expected rank.

Truthfully, that sort of thing could have happened to me in my full-on mad scientist phase last year. I'd run out of glassware and end up using drinking cups from time to time.
Then again, though, it's not possible to drink a strong acid and not immediately detect the extremely sour flavor and try to spit it out. Daddy might get part of a mouthful before spitting it out and realizing with horror what he'd done, and then try to rinse his mouth out as it corroded. The result would be severe burns and tissue damage throughout the mouth and lips but probably nothing fatal. If some were swallowed it would cause severe damage to the esophagus and possibly stomach, but still survivable with modern medicine.
It's pretty hard to die of acid or base exposure, even to the mouth, but very easy to be permanently maimed. That's why they are so popular among revenge-seeking jilted ex-lovers and the like - the attack maims the victim but rarely kills her. In a way, the goal is to be crueler than murder - to leave them alive, but severely disfigured and suffering for the rest of their lives.
I've licked up little droplets of straight phosphoric acid (weaker than H2SO4 or HCl, but still strong enough to be corrosive), fairly concentrated sodium bisulfate (similar to phosphoric in strength - it's a half-neutralized version of H2SO4), and relatively dilute HCl. All are intensely sour and HCl in particular has the same acidic taste as vomit - mostly because stomach acid is HCl.
Here's my overall review of the acids I've played with at home, ranked by how much I liked using them. I'll also include a couple of acids I've not played with in brackets, with my expected rank.
Spoiler Bootstoots' ranking of acids :
1. Phosphoric acid (H3PO4) - The safest acid and still strong enough for most uses. It's viscous enough to not end up getting everywhere, doesn't damage clothing, doesn't reduce or oxidize anything, and so on. Mixtures of it with trisodium phosphate (TSP) can form three great and cheap buffer solutions at convenient pH values of 2, 7, and 12. Only drawback is that it's a weak acid, but it's not very weak.
2. Sodium bisulfate (NaHSO4) - Much like H3PO4, this is a weak-but-still-pretty-strong acid. It's an acid salt rather than a liquid, which has benefits and drawbacks. Can be used for most things H3PO4 can be used for but not quite as versatile.
3. Nitric acid (HNO3) - Now it's time for a big leap into danger. Nitric acid is fun and can be quite dangerous. Many metals dissolve to form their nitrate salts, which are always very water-soluble and can be quite pretty (copper is a beautiful blue, cobalt a deep red, vanadium is blue at first [it's V(IV)] but can be changed to different colors by adding oxidizing or reducing agents). Mixed with HCl, it makes aqua regia, which can dissolve gold, palladium, and platinum. Mixed with H2SO4, you can nitrate things like cellulose or glycerin, which you can then use to have a blast (please don't make more than a few drops). On the other hand, the dissolution of metals releases copious amounts of highly toxic nitrogen dioxide, a red gas. If you do this inside, you may die. I have done this inside and did not die, but it was with pretty small quantities and I was still an idiot. Points deducted for dangerousness, but still awesome.
4. Sulfuric acid (H2SO4) - Ah, the old workhorse acid. This stuff is more dangerous and more annoying than some other acids because it dehydrates everything, including carbohydrate molecules, turning them into soot. Working with it more or less guarantees holes in your clothing - and prevention of holes is the main reason people wear lab coats. But it's strong, dependable, and helpful for some reactions where you want to remove water to drive the reaction forward. Dissolves some metals to form sulfate salts. Oxidizing when concentrated but not as much as nitric acid.
[5. Hydriodic acid (HI) - Presumably even better than HBr. Illegal because it's used to make meth. Plus, HBr is enough for most non-meth purposes. So don't produce this one.]
6. Hydrobromic acid (HBr) - Like an improved version of HCl. This stuff is slightly less volatile than HCl, and it's more fun to brominate molecules rather than chlorinate them because Br comes off the molecule more easily than Cl. And it replaces things like OH- more easily because Br- is a better nucleophile. Great for making alkyl halides. Slightly reducing. Hard to find but can be produced with some effort.
7. Hydrochloric acid (aka muriatic acid, HCl) - Very cheap, and doesn't do anything weird like oxidizing things or dehydrating them. The main drawback is that it's really volatile. The molecule HCl is a gas dissolved in water, and it comes out quickly and obnoxiously, creating corrosive fumes everywhere. Don't store next to any metal things you care about - even an unsmellable amount seeping out from a store-bought bottle will corrode things over time. Can be used to create chloride salts of some metals, and to chlorinate some organics like t-butyl alcohol. Used in aqua regia. I mostly avoided it and used phosphoric where possible, but sometimes you do need HCl.
8. Glacial acetic acid (CH3COOH) - The smell is obnoxious and penetrating, as you'd expect from 20x concentrated vinegar. But it does have some uses like making esters. Then you get fruit smells instead of vinegar smells.
9. Caro's acid, aka piranha solution (H2SO5, plus unreacted H2SO4 and H2O2) - Made by (carefully!) mixing sulfuric acid with concentrated hydrogen peroxide. As its name implies, this stuff eats just about everything except glass and some strong plastics. Even small amounts of graphite or soot can be destroyed, oxidized straight into CO2. Among the most dangerous things I've ever made. But it's great for cleaning glassware!
10. Formic acid (HCOOH) - Augh! The smell is penetrating. Somehow it just smells like corrosion. It's the acid ants inject into you when they bite, and that's where the name came from. Even brief contact will cause your skin to break out into burning hives. It can be used to make carbon monoxide by mixing with sulfuric acid, in case you feel like making toxic gases.
[11. Perchloric acid (HClO4) - Known for exploding unpredictably at concentrations above 70%. Strong oxidizing acid, but seriously, just use nitric, or piranha if you're crazy. Geologists use it to chew up rocks though.]
[12. Hydrofluoric acid (HF) - Such an interesting acid, but I ain't touchin' it. When most acids contact your skin, they just sit there for a few seconds and give you time to rinse them off, then start eating you slowly so that you might get only a little burn, and take quite a while to chew fully through the skin. HF is different. The molecule, being technically a weak acid and chemically resembling water, easily and quickly penetrates deep into the skin, severely damaging everything on its way down, including the nerves that would communicate pain. Then it releases its fluoride ions into your bloodstream. The F- then reacts with calcium in your blood to produce insoluble CaF2. Your heart needs calcium ions to operate correctly. So if you got too much HF, it will go nuts and then shut down, and you die. Also, it's volatile and can do this sort of thing to your lungs.]
2. Sodium bisulfate (NaHSO4) - Much like H3PO4, this is a weak-but-still-pretty-strong acid. It's an acid salt rather than a liquid, which has benefits and drawbacks. Can be used for most things H3PO4 can be used for but not quite as versatile.
3. Nitric acid (HNO3) - Now it's time for a big leap into danger. Nitric acid is fun and can be quite dangerous. Many metals dissolve to form their nitrate salts, which are always very water-soluble and can be quite pretty (copper is a beautiful blue, cobalt a deep red, vanadium is blue at first [it's V(IV)] but can be changed to different colors by adding oxidizing or reducing agents). Mixed with HCl, it makes aqua regia, which can dissolve gold, palladium, and platinum. Mixed with H2SO4, you can nitrate things like cellulose or glycerin, which you can then use to have a blast (please don't make more than a few drops). On the other hand, the dissolution of metals releases copious amounts of highly toxic nitrogen dioxide, a red gas. If you do this inside, you may die. I have done this inside and did not die, but it was with pretty small quantities and I was still an idiot. Points deducted for dangerousness, but still awesome.
4. Sulfuric acid (H2SO4) - Ah, the old workhorse acid. This stuff is more dangerous and more annoying than some other acids because it dehydrates everything, including carbohydrate molecules, turning them into soot. Working with it more or less guarantees holes in your clothing - and prevention of holes is the main reason people wear lab coats. But it's strong, dependable, and helpful for some reactions where you want to remove water to drive the reaction forward. Dissolves some metals to form sulfate salts. Oxidizing when concentrated but not as much as nitric acid.
[5. Hydriodic acid (HI) - Presumably even better than HBr. Illegal because it's used to make meth. Plus, HBr is enough for most non-meth purposes. So don't produce this one.]
6. Hydrobromic acid (HBr) - Like an improved version of HCl. This stuff is slightly less volatile than HCl, and it's more fun to brominate molecules rather than chlorinate them because Br comes off the molecule more easily than Cl. And it replaces things like OH- more easily because Br- is a better nucleophile. Great for making alkyl halides. Slightly reducing. Hard to find but can be produced with some effort.
7. Hydrochloric acid (aka muriatic acid, HCl) - Very cheap, and doesn't do anything weird like oxidizing things or dehydrating them. The main drawback is that it's really volatile. The molecule HCl is a gas dissolved in water, and it comes out quickly and obnoxiously, creating corrosive fumes everywhere. Don't store next to any metal things you care about - even an unsmellable amount seeping out from a store-bought bottle will corrode things over time. Can be used to create chloride salts of some metals, and to chlorinate some organics like t-butyl alcohol. Used in aqua regia. I mostly avoided it and used phosphoric where possible, but sometimes you do need HCl.
8. Glacial acetic acid (CH3COOH) - The smell is obnoxious and penetrating, as you'd expect from 20x concentrated vinegar. But it does have some uses like making esters. Then you get fruit smells instead of vinegar smells.
9. Caro's acid, aka piranha solution (H2SO5, plus unreacted H2SO4 and H2O2) - Made by (carefully!) mixing sulfuric acid with concentrated hydrogen peroxide. As its name implies, this stuff eats just about everything except glass and some strong plastics. Even small amounts of graphite or soot can be destroyed, oxidized straight into CO2. Among the most dangerous things I've ever made. But it's great for cleaning glassware!
10. Formic acid (HCOOH) - Augh! The smell is penetrating. Somehow it just smells like corrosion. It's the acid ants inject into you when they bite, and that's where the name came from. Even brief contact will cause your skin to break out into burning hives. It can be used to make carbon monoxide by mixing with sulfuric acid, in case you feel like making toxic gases.
[11. Perchloric acid (HClO4) - Known for exploding unpredictably at concentrations above 70%. Strong oxidizing acid, but seriously, just use nitric, or piranha if you're crazy. Geologists use it to chew up rocks though.]
[12. Hydrofluoric acid (HF) - Such an interesting acid, but I ain't touchin' it. When most acids contact your skin, they just sit there for a few seconds and give you time to rinse them off, then start eating you slowly so that you might get only a little burn, and take quite a while to chew fully through the skin. HF is different. The molecule, being technically a weak acid and chemically resembling water, easily and quickly penetrates deep into the skin, severely damaging everything on its way down, including the nerves that would communicate pain. Then it releases its fluoride ions into your bloodstream. The F- then reacts with calcium in your blood to produce insoluble CaF2. Your heart needs calcium ions to operate correctly. So if you got too much HF, it will go nuts and then shut down, and you die. Also, it's volatile and can do this sort of thing to your lungs.]