Which cello albums should I buy?

Absolutely no background in cello music, but fell in love with some I heard, and I have a good ear for good music, also varied taste.
That said, I prefer the slower pieces, and like some Hungarian tunes I have heard in passing.
Casals The Birds moved me.

Any suggestions to check out?

Bach's Unaccompanied Cello Suites, which are kind of stark and cerebral

Elgar's Cello Concerto, especially Jacqueline DuPre's recording

Victor Herbert's Cello Concerto

Bachianas Brasileiras by Heitor Villa-Lobos has sections that are for soprano and cello

Antonin Dvorak wrote a couple of cello concertos for his son-in-law, who was a cellist.

There's also a piece by a composer called Popper (forget his first name), for three cellos and orchestra.

Look these up on iTunes and sample them.

Both string quartets and string trios typically include cellos, and a piano trio is typically a violin, a piano, and a cello.

Actually, anything by Rostropovich.

But the Dvorak Cello Concerto is a personal favorite of mine, and his performance of it is stunning.

Rostropovich's complete recording of the Bach cello sonatos also sublime. Yo Yo Ma's is also very good (not sure if Yo Yo has recorded all of them, but I know he's done some, and they're beautiful).

Yo Yo Ma also did a series of videos of him playing Bach Sonatas while some Japanese dancer guy dances some kind of modernistic kind of dance. Those are quite wonderful.

For some real mind-bending cello - especially since you mentioned you like slow stuff - check out Zoe Keating. She does a kind of minimalist/trance/psychadelic cello thing with loops and effects that's actually quite beautiful, and not just electronic tom foolery self-congratulatory masturbation. You can hear her on WNYC's Radiolab here: http://blogs.wnyc.org/radiolab/2008/08/25/quantum-cello/

Speaking of which, you should also always listen to Radiolab.

on the Winter & Winter label. Some of it avant-garde but superbly played, recorded and made.