There's very few minor differences between those two.
Nikon has a consistent mount throughout its current generation of amateur and pro DSLR cameras. If a lens mounts on one, it should mount on the other. On some entry-level cameras with older lenses, you may not get autofocus and/or metering — but the lens is still functional. Nikon used to have only autofocus in the body. Some previous generation lenses require a camera with a focus motor in the body to autofocus. Nikon's recent mirrorless CX-mount differs from it's DSLR F-Mount because CX lenses are not intended for use on DSLRs - but official Nikon adapters do exist to mount F lenses on the CX mount.
Canon current has two mounts: EF and EF-S, and an EF-S lens is made for a APS-C sized sensor and physically won't mount to a full frame camera. (Based on Matt's comment below, it may be possible to mount a EF-S lens on a fullframe camera with some modification to the lenses and a limited zoom range.) EF lenses will work on either APS-C or full frame cameras. All autofocus Canon lenses have focus motors in the lens.
The off-camera flash system is very different between the two as well.
They each have a few lenses in their arsenal that the other is lacking — extreme macro or adjustable soft focus lenses for example. But those are really niche cases.
Canon is making their own sensors and Nikon has started to use some Sony sensors that are shared among several cameras (Nikon D7000, Pentax K-5, and Sony A580 all use the same sensor - or very close to it). The current generation of Sony sensors in these cameras appear to be superior to the current Canon sensors. Most of the technology advantages between the "big two" tends to switch back and forth as they each introduce new generations of cameras - so a sensor advantage today may not exist tomorrow.
Realistically, either would take good pics.
Don't forget about Pentax and Sony as well — they're competing for market share instead of against their own lines and look to be feature packing even their lower level cameras. Canon and Nikon (especially) leave off obvious (sometimes even basic) software enhancements from their lower lines in order to encourage mid-to-top tier purchase.