A key example of this would be Gundam Wing. Gundam Wing's main characters are 5 young men who pilot giant robots called gundams (this anime also is a key example of the "sci-fi tends to have giant robots" part of this description ^^ ). These young men, and everyone else in the series, all have different ethnic backgrounds. Some come from America, another from China (actually a space colony that's like China, but one of them is Chinese, that's the point), and another from a desert type area. However, as this is science-fiction we're talking about, the racial diversity doesn't just end with Earth's ethnicities. There are some sci-fi anime that have different people from whole different planets, galaxies, etc. This genre of anime often has a very diversified cast of characters.
Also, as Science-Fiction Anime is so popular and has so many different series in its genre, it has released what some may call a sub-genre. The sci-fi/fantasy mixture can be seen in a good bit of anime, but the best example may be Tenchi Muyo.
This anime mixes sci-fi and fantasy by taking the typical sci-fi element of space travel, and mixing it with the typical fantasy elements of magic swords, jewels, and demons. So as you can see, Sci-fi anime is popular and very diversified!
*Fantasy Anime*
First, this genre has been known to use already-existing myths and/or fables. Since anime is Japanese animation, fantasy anime has been known to use Shinto stories and other Japanese-oriented myths and/or fables.
However, other types of myths and fables have been used. While fantasy anime has used myths and/or fables, in some cases, these myths/fables are only a "base". Sometimes, the creators of fantasy like to take a myth and combine it with their own ideas to make it more unique. While, as I mentioned earlier, fantasy anime has used Shinto stories, it has also been influenced by Western fantasy-oriented things, such as the popular fantasy role playing game, Dungeons and Dragons. The key example of this would be Lodoss War.
So, fantasy is pretty much the same in anime as it is in, say, books and movies. It comes from myths and fables as well as other ideas mixed in with them.
And since it's Japanese animation, Shinto myths are in a good bit of fantasy anime, Inu-Yasha is a perfect example. However, fantasy anime is also influenced by the Western game of D&D. And that, in a nutshell, is Fantasy Anime.
*Horror Anime*
Like the fantasy genre, the horror genre of anime, is pretty self-explanatory and like anything else with "horror" in it, like horror movies/books. Horror anime is known for its unique creature designs. Also, as can be expected, horror anime is usually very gory. However, unlike the typical gory horror film, it's not gory just for the sake of gore. The gore is very realistic. Let's face it, if someone gets their head chopped off or something similar, there will be a great amount of blood.
Horror anime has also been known to have some sexual material in it. However, don't mistake this for a cheap porn type thing. The sexual material in most horror anime isn't very explicit and, like the gore, it's not just there for the sake of being there. It tends to have something to do with the plot.
So, horror anime is pretty much what you'd expect from anything with "horror" in it. A key example of horror anime is Doomed Megalopolis.
*Comedy Anime*
Now, comedy anime is fun, but there is a downside to it for Americans seeing it. Another thing they tend to do in comedy anime is make jokes that have references to Japanese culture, theatre or literature. For the American who is not so well-versed in these subjects, the jokes will make no real sense and thus won't be funny. Comedy isn't the only anime that does this, but it's probably the anime that does it the most. This is handled differently depending on whether the anime is being subtitled or dubbed into english. If it's subbed, the subtitles tend to include liner notes explaining the reference, although sometimes they won't put anything (maybe the subbers don't even get it? :P ). If the anime is dubbed, the dubbers will most likely just change the original dialogue, and make the joke into something western-based.
The best example of comedy anime that has all the above things in it would be Love Hina. So, comedy anime is there to make you laugh by funny sexual content, cultural jokes, and poking fun at other anime genres or even other anime.
*Romance Anime*
The genre it tends to blend with the most is comedy. In the midst of romance, there will be comedy and vice versa. Romance anime can be for different ages as well.
There is some that is lighter which is for kids/teens and there is very heavy romance anime which is moreso for adults (NOT porn, just that the stories are more complicated and drawn out so adults like them more than younger people).
Examples of pure romance anime include Kimagure Orange Road and Maison Ikkoku. These 2 anime are key examples of what I meant about some romance anime being for younger people and some romance anime being for older people. Kimagure Orange Road is a lighter romance that deals with teens and is for a teenage audience, maybe kids as well, but all around is more for the young people. On the opposite end, Maison Ikkoku has a heavy plot which is more drawn out and detailed. This anime is moreso for adults, not because of any "mature themes", but because alot of younger people would find it "boring". So, romance anime tends to blend into other genres, mostly the comedy genre. The pure romance anime can be for different audiences. There is the lighter types of romance anime which is more for teenagers and maybe kids (like preteens?), but there is also the heavy type of romance anime which is for adults due to its very detailed plots which can be too "heavy" for younger people.
*Shojo Anime*
Shojo (the Japanese word for girl) anime is anime focused strictly on a female audience. Typically, a child to teenage female audience. This type of anime has shows that are very similar to eachother and most shojo anime contains one or all of a few things. First, shojo anime usually has the main character, who is almost always a girl, dressed up in very unique outfits.
Also, these girls who are dressed up in these unique outfits tend to be "magical girls", or girls with special powers of some sort. Shojo anime also sometimes includes a bit of romance. The romance isn't usually very deep like the type of romance you see in the romantic genre of anime. Examples of shojo anime include: Pretty Sammy, and Card Captor Sakura.
*Shonen Anime*
And now for the opposite gender-related anime, shonen (the Japanese word for boy) anime. This type of anime is geared toward male children and teenagers. It tends to be violent, however not extremely so, and action-packed. In fact, most "action" anime is really shonen anime. The violence in shonen anime is also not very gory at all, unlike the violence of the previously mentioned horror anime.
The shonen anime genre's most often-used elements are cars, mecha, and martial arts. Not all of those things are together in the same anime, but just about all anime in this genre has at least one of those elements.
Examples of shonen anime would be the Dragonball series along with its counterparts, Dragonball Z and Dragonball GT.
*Hentai Anime*
Hentai also has a couple sub-genres. There is yaoi hentai which is male with male content. There is then the yuri hentai which is the opposite, being female with female content.
Alot of hentai series tend to include both yaoi and yuri at one point or another.
Hentai is also known for its rather bizarre and realistically impossible things such as monsters/demons having sexual encounters with humans, and martial arts that have a sexual twist. One of the best examples of all the characteristics of hentai mentioned above would be La Blue Girl.
*Adult Anime*
Last, but not leastof the anime genres, we have the adult anime. First and foremost, this genre of anime is not hentai and it is nothing like hentai even though it is also geared specifically for adults. Adult anime tends to have a slow and novel-like structure that is too boring for younger audiences.
Adult anime doesn't have too many overly mature themes that are inappropriate for children. A mature teenager could watch adult anime, however, it is mainly for adults and mainly adults watch it. An example of this genre is Maison Ikkoku.