Well, it seems like I got here a bit late
The explanations given above pretty well cover it, but for a little more detail and clarification I will add this:
Anime: In the US and many other western nations, it is limited to meaning Japanese animation (AKA Japanimation, although a lot of people don't like that term). Characteristic features would be large eyes, funky hair colors, and often, er, accentuated physiology. In Japan, anime means animation in general, Warner Brothers, Disney as well as Macross and El Hazard.
Hentai: The classical meaning is "metamorphosis, transformation." It later came to mean "abnormality," and in modern colloquial Japanese is used almost exclusively to mean "pervert" or "perversion." In adult anime, hentai normally would lend itself to what we consider hardcore images, such as the very popular bondage anime images. In the Adult market Anime has come to signify more softcore images and Hentai hardcore.
Manga: This is what comics are called in Japan. The artist Hokusai coined the word manga in 1815, usually translated to mean "irresponsible pictures." Traditionally drawn in black and white, sometimes with blue inks mixed in, Manga can be action comics, love stories or even hardcore fantasy.