This old computer I've had for a while, I've always run 32-bit systems on. A couple days ago, I happened across something that I wish I'd known before - it's 64-bit capability.
So, here's the simple way to identify whether your CPU is 64-bit capable. Note this only works on Linux, but then, why would you want to run anything else? (BSD might also work, but I don't know for sure. Can anyone confirm?)
You'll need a terminal. Enter the following command:
Read the output, and look for the section on Flags. For my CPU, it looks like this. The bolded part is the one to look for.
processor : 0
vendor_id : AuthenticAMD
cpu family : 15
model : 44
model name : AMD Sempron(tm) Processor 3000+
stepping : 2
cpu MHz : 1000.000
cache size : 128 KB
fpu : yes
fpu_exception : yes
cpuid level : 1
wp : yes
flags : fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 syscall nx mmxext fxsr_opt lm 3dnowext 3dnow up rep_good pni lahf_lm
bogomips : 1999.70
TLB size : 1024 4K pages
clflush size : 64
cache_alignment : 64
address sizes : 40 bits physical, 48 bits virtual
power management: ts fid vid ttp tm stc
Notice in that the list of flags, there's 'lm'?
If you see that in your CPU's list of flags, you have a 64-bit capable CPU.
And all this time I've been running a 32-bit system on it. To think I never knew.
To be fair, switching from 32-bit Ubuntu Karmic to 64-bit Ubuntu Karmic hasn't been entirely smooth. I've yet to manage to get Skype to work, and a few of my other applications don't seem to have amd64 packages, only i386 ones. This is inconvenient, but on the other hand, gets me experimenting with alternatives I don't normally consider, thus allowing me to learn more.
So next time you're sat wondering if you can run a 64-bit system... fire up a terminal (Or if you're not on Linux, grab a Linux LiveCD and use that instead) and run that command, and lo and behold, definite proof.