A lot depends on what settings you want to achieve.
I'm running the sim fine on mostly medium settings on this:
i7 920 @ 2.7 GHz (the very first that came out, no overclocking at all)
Ati 4890 1GB
3GB RAM
Windows 7 64-bit.
I'd say my main issue the low RAM. There was no win7 when i got it and i didn't want to install xp 64bit or vista, so i stayed with xp 32 bit and got just as much memory as it could utilize.
I think that installing another 3GB of RAM would cure a few small problems and help loading times.
Apart from that, if you want to run higher settings then of course you will need a new graphics card.
Just like everyone else pointed however, the system components must match each other. You don't want to spend money on a fast card if it's going to be held back by the rest of your system, or if your OS can't utilize at least DX10.
As also pointed out already, make sure you have a good power supply. Graphics cards can be very power hungry beasts when working at full load and if your PSU isn't up to it, it could lead to crashes.
In my experience, looking only at the nominal wattage for a PSU isn't enough. It's best to get a unit with a slightly lower nominal wattage from a reliable manufacturer and be sure that it achieves it, than get one of dubious quality just because it quotes more watts on the box.
Also keep in mind that bigger wattage doesn't necessarily mean bigger power bills. In fact, it's usually the other way around because most PSUs start to have increased thermal losses the closer they are to their limits. For example, if you have a PC that requires 400Watts and you try it on a 500Watt and a 700Watt PSU, most of the times the 500Watt PSU will waste more power because it's operating closer to its limits.
Generally speaking, most of the PC components can be upgraded with budget solutions, but there are three things you should generally not skimp on: motherboard (for upgradeability), PSU (for optimal power delivery and fail-safe features) and monitor (for easy and tireless viewing).
These are not only important for your day to day PC usage, but also don't require as frequent upgrades as other components, so it makes sense to pay a bit extra and be set for a longer time. I've had a case where my PSU saved my system, when a power surge/spike occured. The PSU died and got replaced thanks to warranty, but everything else in my system survived.
