I found a good price on a Rebel X. It comes with a flash and a couple lenses. Could I use those accessories with most new DSLR cameras? Would I be limited to Canon cameras?
Rebel X (EOS-500/Kiss XS without pop-up flash) is a fairly recent entry level body. It uses EF lens mount, so the lenses should work fine with current Canon DSLRs. The flash hot-shoe is also compatible with current models, although Rebel X did not support E-TTL. The flash will work on a Canon dSLR, but the features it will offer depend on the flash and cannot be determined from model number of the body. Any EX-series flash can be used with E-TTL metering.
The lenses can be used on Canons, and any other camera system (e.g. micro four thirds) that has adapters for Canon EF lenses (with limitations imposed by the adapter). The flash can be used in manual mode with any modern dSLR (except Sony/Minolta); advanced features, if there are any, can only be used on a Canon.
would they work on new cameras? Most likely not or with limited functionality (depending on how old the model you're buying is, I'm not familiar with the American model names Canon uses).
Would you be limited to Canon cameras? For the lenses, yes. The flash would probably (but not guaranteed, some flash units require special signals to work that can be brand specific) work, again with limited functionality, on most other cameras (you'd effectively lose any metering and timing synchronisation between camera and flash, have to work in full manual mode).
Mind this isn't Canon specific, the same is true for other brands as well. E.g. older Nikon flash units won't work on newer DSLR bodies (except possibly in full manual mode), older Nikon lenses may have limited functionality (what you get depending on the lens/body combination) on newer bodies.