Before I reply to anyone I want to state that when I said 'staraffing' I just wanted a term that would represent some kind of ground attack. What I meant was any attack that does not include high altitude bombardment --not limited to guns only. This keeps with the simple nature of CIV; i.e. technically a unit is not just one guy, it reperesents a group.
The fighter cannot kill any units.
This would defeat the purpose. In WW2 fighters would not pick off every single last guy on the ground, but a surprise attack could potentially decimate a group to virtually nothing --CIV is not that exact: if you win, it's the equivilant of killing most of the guys to point where they are just scattered survivors; i.e. a few guys don't constitute a unit.
Although you're right, ground attack is usually only partially successful, while the Fighter shouldn't die just because it missed.
Placing artificial limitations on air-ground combat will tend to be complicate things, so why not just give the Fighter a retreat ability, thus preventing it from being destroyed if the ground units is winning?
I think the simplest solution would be to just take away the Bombard ability from the Fighter so that players have no choice but to risk losing the unit --after all, WW2 Fighters would rarely bombard from high altitudes; i.e. they either dive-bomb or make low-level flight and drop right before getting to the target. Of course, this just means that if they have a choice, players will use their Bombers instead. The only reason not to would be that the Attack Mission never fails to get a hit, unlike Bombardment. Yet the risk of losing the Fighter is still worse than a failed Bombardment.
As you can see, the reasons for simplifying the Attack Mission are clear. By just using normal combat, the Fighter has an advatage over the Bomber in an assured kill (if it wins) in addition to an assured hit. I would personally just give the Fighter the retreat ability, thus having the fighter pull out if things get too hairy. It's nt as realistic as your idea, but its keeps with CIV's simplicty.
From a game play balance, this would tend to be too powerful; players could simply send fighter after fighter to attack units before they can even get close!
The purpose of allowing ground units to counter-attack is precicely to prevent the Fighter from being too powerful. If you attack with any other unit, the same thing happens the only difference is that a ground unitcan't fly back to base after attacking. If you know they're coming, you will bombard them, so why not Attack them too?
The fighter will attack ALL units in the stack.
Bombardment in SMAC does that. It implies 'collatoral damage.' Considering some of the people who worked on that also worked on Civ3, I never understood why Civ3 Bombardment doesn't work this way.
So, if anything Bombardment should do that, whereas Attack is more specific. Its assumed that the various units (i.e. groups of guys) are separated, so the fighter would have to go from one to another --don't take CIV too literally.
The fighter can only do up to one point of damage to each unit in the stack.
To similar to non-lethal Bombardment. It would just make the Fighter's attack inferior to Bombardment.
...so that the unit does not outclass other units (ie, radar artillary) in every way.
Other units have different functions. The idea behind the Fighter is that it has the ground unit's ability to attack and and the air unit's ability to do so though Air Missions. Artillary units are differnt from Bombers because they are ground units, nothing more. Fighters are designed to finish off units on the ground and to provide air cover. The way to duplicate this is just to give the Fighter a low Attack thus heavily-armed ground units can wear it down and cause it to retreat before it kills them. This essentially has the effect of limiting the Fighter to the effect you suggested, without adding in any extra air unit attack rules.
The fighter can be attacked by any and all units in the target square.
That's getting into the issue of grouped (i.e.simultaneous) unit attack/defend. CIV should be able to do that, but can't. So, although it is a good and sensible idea, it can't be done at present.
Units in the stack may only do up to one point of damage each on the attacking fighter.
That can be more easily addressed by giving the Fighter a retreat ability when its health goes into the red, as stated above.
...units in the stack CAN destroy the fighter if it runs out of hitpoints.
I refer you to my reply concerning groups.
How would this work when straffing sea units and would the ship get to counter attack? Based on the ship this may or may not be possible. Maybe wooden ships could not counterattack but modern ones could...
Any ship with the Ranged flag and A/D factor could counter-attack. Older ships have low defense and fewer hitpoints, so the Fighter would kill every time. Modern ships would defend just like any Ranged land unit.
(I was thinking that for scneario purposes, a "100% Attack vs. Ships" flag could be given to Torpedo Bomber units.)
Maybe a new category called strafe...
I think that's getting a little too specific for CIV. Besides, there is not need since Bombard Missions weaken (and sometimes kill) and Attack Missions kill (if they win). The flag thing would have some useful applications.
BTW, is it possible for modern jet aircraft to strafe???
Yes, but they tend to over-shoot, especially in the early days.
If this is a mission, would this happen automatically everytime a unit is within range,
It would work the same way Bombard Missions do.
I am also worried with the low attack value of fighters that they would need a bonus when straffing (maybe 100%) or they would consistently lose to any unit with a defense of 6 or higher...
If my suggestion is used, the Fighter will retreat if close to death. But will have an easy time with weak ground units.
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To give you all an idea:
Picture Bombers weakening enemy ground forces and Fighters moving in to finish off whatever's left.
Isn't that essentially how it works in reality?
Some good replies. I'm interested in ideas concerning air combat flags, any suggestions?
I love anything to do with fighters (see avatar 
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