Anime is most commonly based off of a manga, which is basically the Japanese word for comics. Usually when people call something manga they mean that it was made in Japan. Some people prefer manga over anime and vice-versa but the two are usually quite closely related to one another, if not directly following one another, although in almost all cases the manga comes first before the anime. Unfortunately I am not a fan of the genre so I don't have much expertise in reading it, of course with my love for anime I have given manga a chance here and there but it will never be as good as anime to me. Manga is becoming increasingly popular in many parts of the world including the United States. Manga often comes in magazines that will include a few chapters of several different series, some daily, some weekly, and some even more spread out or even produced randomly. While not all anime is based on manga, I would venture to say that at least 90% of them are. It is not uncommon for an anime to be produced at the same time as the manga it is following, however this often leads to the anime catching up to the manga too quickly which forces the anime creators to either go on a hiatus or create 'filler' episodes that have no real connection to the overall storyline. One problem that this creates for fans of anime but not manga is that the manga is always ahead, thus the people who read it will know what is going to happen before the anime viewers will, one of the many reasons I have almost always avoided anime discussion forums is because of the spoilers that manga readers inadvertently blurt out and may ruin months of anime viewing for me.
That's not all though, anime is also very commonly based on video games, and some even have entire franchises of video games based on the anime. One of the best examples I can think of for this is Star Ocean: EX, the anime almost follows the games storyline and cinematic perfectly, some people may not realize how powerful of storylines some video games have within them, and to have the entire thing presented to you visually can really be quite stunning. Some other great current examples of games turned anime are Final Fantasy VII: Advent Children, Valkyria Chronicles, Gungrave, Devil May Cry, Pokémon, Sonic the Hedgehog, Street Fighter, and many more. It was actually a misconception of mine for the longest period of time that the Pokemon anime came before the games, it wasn't until about five years later that I realized how wrong I was. Those are just a select few that were in many cases beloved video games of my childhood that left me wanting more, having an anime to watch that continues or gives me more plot and story is always a beautiful thing. A full listing of anime based on video games is kept up-to-date on Wikipedia, the link is provided. http://en.wikipedia.org/wiki/List_of_anime_based_on_video_games
Of course, some anime are even original creations, these however require far more work than simply taking comic strips and animating them together (not a proper explanation of the manga to anime transformation but the gist of it). Original creations require, at least in my opinion, a truly visionary person to create them. OVA's, or original video animations, while sometimes based solely off an anime of the same name but created by another animation organization, are the most commonly seen forms of original anime content. Most OVA's are short in length ranging from one to five episodes each, but then again in some specific cases there are others that are anywhere from 10-100+ episodes in length, obviously this is a factor of how much time and work goes into them. Currently I am following two anime OVA series that are around ten episodes each in length but rather than weekly episodes they only release about one episode every six months, that's right I said six months between episodes. Obviously this sounds like a pain, but many OVA are considered to be better than their parent story anime by a large amount of the anime viewing public.
Not surprisingly some anime even evolves one step further into having a live-action movie or series made based on it. Many of the more popular anime have spawned off live-action creations such as Gantz, Dragon Ball, Detective Conan, Cowboy Bebop, and Great Teacher Onizuka. While the success of these live-action movies hasn't been spectacular, it is quite a different watch and gives you a better look into the capabilities that anime has over what special effects can do for a movie. Having seen the live-action Dragon Ball, Detective Conan and Great Teacher Onizuka movies and other specials, I must say that I was quite disappointed with them, but mainly due to bad acting and low budgets. Earlier I mentioned the Cowboy Bebop live-action movie, which is still in development at this point, but looks promising with The Matrix star Keanu Reaves playing the main character Spike Spiegel, that alone puts it over the seemingly random set of actors I have seen in other live-action things. Hopefully Cowboy Bebop does well in American markets so we see more big name actors starring in live-action anime based movies, it's my belief that things are leaning that way since I've noticed an increase in actors like Tina Fey, Matt Damon, Andy Richter, and Will Arnett amongst many others doing the voice-overs for major anime movies (usually the ones made my Studio Ghibli) in an attempt to bring a wider American audience to anime. I actually watched one of Studio Ghibli's movies recently, Ponyo on the cliff by the sea, in English and was overjoyed when I was able to recognize popular television and movie actors voices, however that movie is packed with stars including Tina Fey, Matt Damon, Liam Neeson, Betty White and many others, which was very unlike the usual one or two actors you may recognize.