Recommending a universal camera is impossible; every photographer has different needs. That said, if you're looking at a general gift guide like this one, we can make some assumptions: that you're is not a super-experienced photographer (because otherwise you'd have very strong opinions and probably own all necessary gear already) and that you already have a phone. So! No need for a point-and-shoot; modern smartphones are perfectly up to the task of quick shots. For learning about photography and getting some killer photos in the process, I (with the help of PopPhoto.com editor Stan Horaczek) recommend the Sony NEX-3N, a mirrorless camera that is very capable and crazy cheap.
The NEX-3N has interchangeable lenses, compatible with a rapidly growing suite of Sony NEX lenses, and its image quality was rated "High" in Popular Photography's brutally difficult tests
. It's small and attractive, it takes great shots, and it's affordable.
DSLRs are amazing pieces of kit, but given the quality, ease of use, and portable size of all the new alternatives like the NEX-3N, DSLRs are increasingly only for experts
. That's not to say "don't buy one," it's just to say that if you want great pictures and don't necessarily plan on becoming a lens-hoarding photog, mirrorless is probably a better option.
Buy: Sony NEX-3N
($400, with kit lens)