As King_niral said, you can run a 32-bit OS with 64-bit hardware. But I believe what varun was asking is about 64-bit apps. The answer to that is yes, you'll need a 64-bit OS to run 64-bit software, but that's still some time in the future.
Let's take a look at a few examples of configs that I assembled recently. All RAMs are DDR400, all HDDs are Seagate Barracuda 7200rpm PATA, all optical drives are Liteon, all mice are optical, all monitors are Samsung :
1. Socket 754 2800+
K8MM-ILSR mobo with onboard graphics (OK for non-gaming apps)
128MB RAM, 40GB, CD-ROM drive, FDD
Plain keyboard, mouse, stereo speakers
15" monitor
.... 20k.
2. Socket 754 2800+
K8MM-ILSR mobo, FX5200/128MB
256MB RAM, 80GB, CD-writer, FDD
Plain keyboard, mouse,
17" monitor, 2.1 Mercury speakers
.... 27k
3. Socket 939 3000+
RS480M2-IL mobo, onboard graphics (about the same as FX5200)
512MB RAM, 80GB, Liteon CD-writer, FDD
MM Keyboard, mouse, 2.1 Mercury speakers
17" flat magic-bright monitor
.... 30k
4. Socket 754 3000+
K8N Neo FSR mobo, FX5200/128MB (This was for video editing, not gaming)
1GB RAM, 2x120GB, DVD writer, CD-writer
MM keyboard, wireless mouse
2.1 Creative speakers
DV-AV capture card, TV tuner
19" monitor
.... 63k
These are just examples. Note that none of the above configs is specifically for gaming. For a gaming rig, I'd change some of the items in each price class.