You can run
swapon -s to see what devices and files are being used for swap. For example, my scientific linux machine says:
[firstname.lastname@example.org ~]$ swapon -s
Filename Type Size Used Priority
/dev/sda3 partition 8388600 833408 -1
So I'm using /dev/sda3 for swap. Also note the priority field that can be used to adjust the order in which swap pages are allocated (see
man 2 swapon).
As some folks have stated, if you run out of swap (or have zero swap) the OOM Killer may start killing processes when physical memory gets low.