Most commonly sourced from animation (both North American cartoons and Anime), since by nature animated characters are designed to be easy to draw. People with an interest in visual arts are also more likely to be animation fans than most others.
As for live action shows, it takes a certain level of artistic sophistication to depict real people with any degree of recognition. That doesn't stop anyone, however, and any visually interesting or unique show is likely to have some fan-made pieces floating around. Most often these are Speculative Fiction shows, since most fan art based on normal people is more about the actor or actress than the character. Then again, an entire Yahoo! Group is dedicated to celebrity likenesses made with the Poser and FaceGen applications.
In Japan, Fan Art in manga form, from either anime or other manga, are called Doujinshi. Technically, doujinshi can refer to all independently published manga, but to American anime fans it usually means a fan-made parody or erotica based on an existing work.
Of course, there's always Rule 34.
Many Web Comics (particularly ones with recurring characters and good quality artwork) have dedicated fan art galleries on their websites, with images ranging from single characters to full-blown guest strips that don't fit in the archive.
See also Cosplay Fan Art, Rule 63 (for characters drawn as the opposite gender), Side-Story Bonus Art (official art), Self Fanservice (when canonically unattractive characters look better in the Fan Art).
- See DeviantART for a large amount of Fan Art (as well as a wide range of original pieces). Beware, though -- Sturgeon's Law very much applies. Searching people's favorite artwork galleries can help a lot in finding good work, even more if you share the same taste than those people. If you like someone's artwork, consider checking their "favs".
- For a different kind of fan art also see vgboxart, a site/community that focuses on the creation of Fan Art in the form of covers. It started as a site for video game boxes (hence the name), but now it can be described as generalentertainmentboxart as works vary from games to movies to books. All sorts of Cover Tropes apply for the fan work seen there, a lot of uploads are actually good, and a select few are much better than the official packaging seen in stores.
- As mentioned above, a lot of webcomics have Fan Art sections. For example, Gunnerkrigg Court, El Goonish Shive and Zap!.
- Furaffinity has an entire category dedicated to "Sonic" art due to the enormous dump of Fanart. Sturgeon's Law applies liberally to this one.
- Some Image Boards, like the dreaded 4chan.
- The page image for Ryu and Ken shows fanart of, well... Ryu And Ken.
- A notorious historical example was a couple of Snow White fan-drawings found in an old cellar. They were found in Norway, dated to the late 30s, and were signed by a talented amateur artist called "Adolf H."...
- Mr. H. apparently was a major fan of Disney, and he drew a couple other works too.
- Ex-SNK artist Falcoon began his career at that company by drawing fan art for their various properties, such as The King of Fighters and Fatal Fury.
- The careers of Jim Lee and Rob Liefeld both began with them being noticed for their detailed fan art.
- Averted hard for Ctrl+Alt+Del: A fan once made a little CGI movie using Tim Buckley's characters for a school assignment and Buckley threatened him with a lawsuit because he wanted to save his artwork for The Animated Series. Oddly, there was an earlier post from Buckley saying it's okay to make fanart... Naturally this only pushes the Hatedom to new heights of hilarity (usually involving a "Loss Edit").
- Older Than Radio: The works of William Shakespeare have inspired art for hundreds of years, perhaps most famously Sir John Everett Millais' painting Ophelia.
- A remarkable amount for Kim Possible, encompassing crossovers, the KP cast in other roles, Kim and Ron in the future (in college, married, with kids, or just older) and a lot of Kim and her nemesis Shego in a lesbian relationship. Curiously, though Rule 34 obviously applies, the last often tends toward being cute rather than overtly sexual.
- There's a website called "Rule 34 - If it exists there IS porn of it". Guess what it's dedicated to. We're not going to link to it.
- Homestuck, naturally, has a ton of fan art but what makes it unique is that it also has fan music, enough for an entire (free!) unofficial album which is a fraction of Tindeck's Homestuck "genre".