There is a lot of animes in my top but I guess my #1 is:
Code Geass- the only show I have watched and enjoyed all the way through twice. (also see avatar)
Though there are a lot of other favorites: Bleach,Death note, One Piece, Baccano!, Trigun, Inuyasha, GTO, Yu Yu Hakusho, FLCL, probably missing a few favorites.
Movie: Paprika and bleach only anime movies I have seen, so I choose those.

i say my favorites are the World God Only Knows, Sword Art online, Bakemonogatari(and its sequel), Death Note, Joshiraku(it's hilarious)
I think my favorite anime movie is the Haruhi movie, the endless eight made me not put the show in my favorites.
One my favorite newer mangas which is turning into an anime soon is Maoyuu Maou Yuusha.

Technically, "anime" is simply short for "animation", which is how the word is used in Japan.  There, "anime" encompasses all animation, no matter the origin.

However, "anime" has become a loaner word in the west, and is here considered to be only animation produced by a Japanese studio (though the actual work is sometimes performed in other countries such as South Korea).

So, really, both can be correct in the right context.

Also, that definition is off, since most anime probably would not be thought of as science fiction.

I always get shit for this one:

Favorite Anime
1) .Hack//Sign

I used to play a a MUD called Dragon Realms a very long time ago. One of our "friends" just disappeared one day and we tried at first to figure things out "In Character" eventually going OOC and .Hack really reminds me of how much fun that was.

Favorite Anime Movie:
SteamBoy and Howl's Movie Castle

Seen them both so many times that is really hard to figure out which one.

Watched The Secret World of Arrietty recently and thats another great Anime Movie

Favorite anime- don't have one but have favorites
Outlaw Star
Fullmetal Alchemist: Brotherhood
Cowboy Bebop
Mobile Suit Gundam Wing
G Gundam
Zoids
DBZ
Samurai Champloo

Favorite anime movie: Princess Mononoke

My favorite anime series is Clannad (both) and i currently don't have a favorite movie.

DBZ and Death Note are the only ones iv really watched

DBZ, InuYahsa, Crest of the Stars... It is truly a toss-up...

Favorite Series ~ Trigun
Maybe not as awesome as the manga but Trigun has always been my favorite.

Favorite Film ~ Nausicaa of the Valley of the Wind
It can be hard to choose my favorite Ghibli film, but this one always seems to edge out the top spot. As for non-ghibli I'd probably have to go with Akira.

Anime is a cartoon in japan, it means animation. Anything can be an "anime" as long as it's animated.