Dobro is usually played with the instrument held horizontally; slide guitar can be played either way.

If you want to hear some truly incredible slide guitar playing check out Kelly Joe Phelps. He is other-worldly. A perfect combination of voice, instrument and spirit coalescing into a pure aural sensation. I cannot overstate how exceptional (not like anyone else) this guy is.

There are a lot of traditional players but I'd like to mention some contemporary slide guitarists that are noteworthy (pun intended)
Chris Whitley is a great writer and player, but he tends to get pretty electric. Sometimes I like the bite and sometimes it is much too abrasive.
Keb Mo is wonderful. He plays da blooz without playing the cliches. It's hard to be both traditional and contemporary, but this guy does it.
Bonnie Raitt. Her earlier stuff is even better than the newer stuff that made her a star. Her first release is her most acoustic one and her live one ("Road Tested", or something like that) displays all of her sides. She is one of the few people who can do justice to Richard Thompson songs.
Ryland Cooder. What can you say? Check out his playing on his own recordings or on John Hyatt's "Bring the Family" or on the "Little Village" recording.
Finally, in the field of country-soul-Texas-Blues, is LeRoy Parnell. I love this guy's stuff. His first release rocks; it is country played with incredible soul. His Nashville hit stuff is more MOR, but you can't hide that kind of talent, even under Nashville production values.

There are lots more (Leo Kottke, Duane Allman, Norman Blake). It seems all slide guitarists have truly personal, unique "voices" on their instrument. The way they tune the guitar, the way they pick, the type of slide they use, the amplification system - so many elements to add to the uniqueness of the sound.