SIGILL (signal 4) on P3 using 2.2.x kernels:

Problem: kernel 2.2.x doesn't have proper (working) SSE support

Solution: upgrade kernel to 2.4.x

Workaround: ./configure --disable-sse

General SIGILL (signal 4):

Problem: you compiled and run MPlayer on different machines (for example compiled on P3 and running on Celeron)

Solution: compile MPlayer on the same machine where you will use it!

Workaround: You can forget all this by configuring with the --enable-runtime-cpudetection option or you can disable particular CPU instruction sets with more specific options (like --disable-mmx, --disable-3dnow, etc).

Crashes when dumping streams:

Problem: core dump

Solution: Don't panic. Make sure you know where your towel is.