Seme (attacker): The "active" partner, or top. Sometimes tachi, "sword" (or from tachiyaku, male roles in kabuki), by analogy to gay slang. (Seme and Uke come from martial arts terms.)
Uke (defender or receiver): The "passive" partner, or bottom. Sometimes neko, "cat", by analogy to gay slang.
Riba (from "reversible") or Seke (portmanteau of the above): The "Both" partner who can go both ways; relatively rare but exists.
Sou-seme ("total seme"): A guy who can't (or won't) be anything other than a seme.
Sou-uke ("total uke"): A guy who can't (or won't) be anything other than a uke.
Seme x Uke: Standard.
Uke x Uke: Both guys are uke types. Sometimes called homoyuri (homo + yuri), the leadup becomes slower, and neither of them feels the need to be dominant, regardless of who's on top. Sometimes sudden moves are made by one of them in an attempt to get things started, but it's not long before their relationship is balanced and gentle again.
Seme x Seme: Both guys are seme types. The ride is much rougher than Seme x Uke, as both guys fight to maintain dominance. Eventually the balance is achieved, but the relationship moves more boldly than other kinds.
Example: Iwaki and Katou from Embracing Love (which started off as a one-shot in a Seme x Seme- themed anthology).
Riba or Reba: Reversible couple; the guys could switch roles and have it still work.
Example: June/DMP just released an entire anthology on this theme, called Reversible.
Wanko-nyanko ("doggy-kitty"): The seme is faithful and devoted like a dog (a wanko or hetare wanko) and the uke is temperamental and demanding like a cat (tsundere or an ojou).
Kinniku (buff or muscular): More heavily-muscled types than the usual slender bishonen. Quite common in the Bara Genre.
Kakkoi buaiso (kakkoi = cool, as in Rule of Cool, buaisou = reserved, quiet) seme: Good-looking, stylish, aloof, doesn't talk much. One of the most common seme types.
Hetare (incompetent or loser) seme: Wimpy, meek or undemanding, he may not have the nerve to make the first move, and once things get underway he's probably under the uke's control. Often also wanko. Usually paired with one of the more aggressive uke types.
Wanko (puppy) seme: Devoted and determined, he will fawn on his uke like a puppy and doggedly pursue the uke until he gets him, despite constant rejection. Het equivalent: Dogged Nice Guy, only the BL version is usually nicer (not to mention better looking). Usually paired with a tsundere or cool beauty uke.
Example: Dee from FAKE who is also a toshishita being younger than Ryo by a year.
Tennen genki (tennen = natural, genki = energetic) uke: Cheerful, straightforward and upbeat. Usually The Ingenue. Often Keet. Equivalent to the Generic Shoujo Heroine. The most common uke type.
Example (possibly the most famous one): Shuichi from Gravitation.
Sasoi (seductive) uke: Puts the moves on his seme. A good match for a hetare seme, since the relationship might otherwise never get off the ground. Like other forward types of ukes, might be an Aggressive Submarine.
Osoi (rapist) uke: Just what it sounds like. Rare.
Ojou (queen) uke: Beautiful, elegant, and strong-willed. May be arrogant, demanding, or expect to be treated like royalty. Likely to be from a wealthy and/or traditional family. Frequently tsundere. Het equivalent: Ojou.