Will this computer run new games?

[wolfsrain]

If you are not on a budget, buy a Geforce 8800GTS(the 640MB video memory version, not the 320MB video memory version). Or even better the Geforce 8800GTX(768MB video memory).
The Geforce 8 series are DirectX10 compatible(unlike the Geforce7 series which are not).
If you are on a budget, the GEforce 8500 or 8600 are good choices.
Everything else is pretty good, though more CPU power is always welcomed. Check your Motherboard manual and see if you can upgrade the CPU in the future( in the manual are specified the CPU's that will work on your Motherboard).
The amount of RAM should be OK until you migrate to Vista(if you do that, make sure you have 4Gb RAM, as VIsta recommends at least 1gb for itself).
Your monitor seems to be HD compatible, which is a plus. The hard drive is fine and you can always add another if this won't be enough.
Make sure you have good Power Supply Unit(620W should be enough you go for Geforce8800).
Everything else can come later(a good sound card - Creative X-FI gamer is very good at the price/performance, and a good sound system)