MOST IMPORTANT to least important resource

[corgiman]

Iron
gotta have iron on the higher levels to get through the middle ages competitively. You need it for swordsman (immortals), knights, pikemen and railroads. Production bonus from railroads is an essential to unit and improvement output.

Oil/rubber
This combo is pretty much essential if you can't win the game with cavalry. Many of my games (King/Emperor level) are won with cavalry, so in those cases, oil and rubber never even show up. If you're playing on large/huge world, however, you're probably not going to win until the age of armor, so these two resources are very important.

Horses
Early/mid game domination require, in my experience, some kind of mobile units and that means horsemen and knights. Obviously, my predilection for cavalary units requires horses, so in some scenarios, I would put horses above oil and rubber.

Coal
Nice production bonus that comes in handy right about the time that you need to kick up the unit production to finish off your mid game opponents or rebuild/build a modern army

Aluminum/Uranium
Value is dependent on your strategy. I avoid using nukes in my games because of the damn pollution and political ramifications. Gotta have the U235 for alpha centauri, though. I don't use planes much, so I don't care about aluminum....I'll trade it for lots of cash if I can. Jet fighters don't stand up well to tanks

Saltpeter
Unless I'm sandwiched between much larger, more aggressive opponents which happens a lot on emperor level, I don't care about saltpeter. If I get it and can build musketeers, great, if not, I generally take my chances with pikemen...Fortified in a city they do pretty well.

 

[Jamesds]

You need most of them at some time or another, but I'd say rubber is the most important, then oil, aluminium, coal, iron, horses, uranium, saltpeter.

Or something along them lines

 

[Baltimoretrader]

I tend to be a very militaristic leader, so I'd have to say that the most important resource is iron. It lets you build swordmen which can easily defeat warriors and the like. The second most important is saltpeter for me. I generally pick the advancements that lead to stronger military unit development and quickly build cavalry and upgrade existing units. Once I get infantry its all over for the other civs. You should be able to get gunpowder and saltpeter before the other civs if you pick the advances right. Horses are next on my list (cavalry) are are fairly common on the map. The rest of the resources will appear after you have developed a pretty good sized empire, and you should gain control of oil,rubber, and coal as you learn how to use them.