# uname -p
x86_64

You can also try:

$ uname -m
i686

i686 (or any garbage) = 32-bit
x86_64 = 64-bit

cpuinfo

# cat /proc/cpuinfo
flags		: fpu vme de pse tsc msr pae mce cx8 apic mtrr
pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm
pbe syscall lm constant_tsc arch_perfmon pebs bts rep_good pni
dtes64 monitor ds_cpl vmx est tm2 ssse3 cx16 xtpr pdcm lahf_lm tpr_shadow
bogomips	: 4255.87
clflush size	: 64
cache_alignment	: 64
address sizes	: 36 bits physical, 48 bits virtual

The “lm” flag stands for Long Mode. This means your CPU is 64-bit capable, but does not necessarily mean you’re running a 64-bit operating system.

You can read more in this file:
/usr/src/kernels/#.#.#-#.#.fc11.x86_64/arch/x86/include/asm/cpufeature.h

#define X86_FEATURE_LM (1*32+29) /* Long Mode (x86-64) */

lshw

# lshw
     *-cpu
          description: CPU
          product: Intel(R) Core(TM)2 CPU          6420  @ 2.13GHz
          width: 64 bits

From the lshw manpage:

lshw is a small tool to extract detailed information on the hardware configuration of the machine. It can report exact memory configuration, firmware version, mainboard configuration, CPU version and speed, cache configuration, bus speed, etc. on DMI-capable x86 or IA-64 systems and on some PowerPC machines (PowerMac G4 is known to work).

Source:

https://help.ubuntu.com/community/32bit_and_64bit