Wow... that's tough, most of them are pretty important...
I'd say:
1. Oil
2. Aluminum
3. Iron
4. Horses
5. Rubber
6. Saltpepper
7. Coal
8. Uranium
Oil is needed to build almost everything from the Industrial age on. Period. Aluminum is needed for most of the modern units. Iron is needed to have any sort of chance of surviving in the ancient and middle ages. Horses are needed for the knight which is one of the best unit in the middle ages, the only one that would probably kick it's rear is the Calvary. Next, is rubber, which is needed to build Modern Armour. If you want to wage war in modern times, you NEED this. You'll never take a city without them. Saltpepper is required mostly for sea going units in the medevial age, the only real reason to need it is the Calvary, but unless you were fighting a hoard of Calvary, you could probably survive with just Knights. Coal is needed for about one (maybe two) units. Uranium is used for tactical nukes, ICBMs, and nuclear submarines. I really don't like to use nukes, at all. They really are pointless unless the city you nuke as MANY units in and around it. And nuclear submarines are the same as submarines except they can go one extra square and carry nukes, but, like I said, I don't like those things.
Of course, this is totally in aspect of units. You also have to take into consideration that some city improvements need certain resources. And I don't have a chart for that handy

So I don't know what needs what... I just tend to shy away from Nuclear power plants also, because of the chance of a meltdown and the fact you need a fresh water source. That's the only other reason I can think of that you'd need Uranium... Again, I don't have a chart handy, so I don't know for sure.
-edit-
Hm, I guess you need coal for railroads... Railroads arn't totaly neccisary though, they really pretty much just help you save time if you want to mount an attack

Roads should be suffce, you just want to avoid becoming under seige, because without railroads, it can take time to move your troops to where you need them... So if you see a relation crumbling into war, move your troops to the front (assuming you don't have railroads) To save time, so when war IS declared on you, your troops are already where you need them to be. But if YOU are declaring war, you should have your army built long before you ever declar war. Your enemy will probably be too busy trying to fight you off to try and attack your motherland, thus elminating the NEED for railroads
