I would like to run Windows XP as a virtual machine on my Android tablet. Since Android is based on Linux, is it possible to compile VirtualBox to run in Android? If not possible, is it possible to run WinXP as a virtual machine in any way on an Android tablet?
Have a look at qemu. Apparently it's known to run on ARM. Running XP (if it even works) is probably not going to be a pleasant experience due to what's noted by Chris Herbert and the probable lack of a screen/pointer driver. If you really want to do it maybe wait for the Intel Atom (x86) based tablets. There should be some Atom based Windows 8 tablets about now. The androids are coming soon.
VirtualBox uses virtualization, which isn't possible when the host device (Android tablet) uses a different CPU architecture than the guest device (x86 PC running windows XP). Since your android tablet almost certainly has an ARM CPU, the x86 CPU would have to be emulated, which is massively slower than virtualization. It doesn't seem like it would be practical at all.
You can use any QEMU (x86) emulator for android. It works on comuter, tablet and smartphone. Emulator not exist in google play. Download it from emulator official site (.apk).