Someone who >definitely< knows should be along shortly...
Do I qualify?
There are two compatibility issues to consider -- the region coding and the NTSC (American) vs. PAL (British) video format.
Although British TVs which will accept an NTSC video signal have become quite common in recent years, the reverse is not the case, and very few domestic U.S. TVs will accept a PAL signal.
However, the NTSC/PAL coding only comes into play if you are connecting the DVD player to the TV via an RF link, a composite video link, or an S-video cable. If you link them together using RGB direct video, then it will normally work.
There are still minor differences in the vertical and horizontal scanning rates between the two systems, but these are generally well within the range with which the set can cope.
Is there a difference in TVs? I ask because my cousin has a VCR that plays both PAL and NTSC, and I was thinking of getting one, too. I always thought it was just the DVD or VCS player...?
Pretty much the same answer as above. If you're connecting the VCR via S-video or composite video, then the TV needs to be able to work with NTSC signals. On a direct RGB hookup, it will most likely be fine even if it isn't specifically intended for NTSC as well as PAL.