Can i run Windows 7 64 bit?

i want to run 64 bit windows 7 on my pc...my config is as follows:
Intel Core 2 Duo E7300 2.66 GHz
Intel DG31PR motherboard
2*2GB DDR2 800MHz RAM
Nvidia GeForce 9500GT 1GB Video Card

can i install x64 on this config ...can i play all the latest games in x64? what problems i may get....do i need to back my data in other drives also....even if i am formatting system drive only...

Please answer these queries....

Yes you can run it. Can you play all the latest games? Maybe, maybe not.

Backup is never a bad idea.

i forgot to update system spec in profile...sorry for that...but now i have 4GB RAM....so will it run fine with this spec...what benefits i will get? pros and cons of switching to x64 wuth this config? i dont get it why i need to back-up my data in other partitions when i will be formatting only system drive only to have a clean install....still confused with this...

The benefit is that you can use all 4GB of RAM.

Backup is not mandatory. Only a smart idea.

what about gaming performance? and can i run 32 bit applications in compatibility mode or something like that? and most importantly will i see considerable change in performance ?

It depends on the game. Some perform better in 64-bit, some worse.