Has an anime ever come out before the manga was published? I got into a debate with a friend about whether or not it's possible for an anime to come out before its manga.

He claimed that there were several instances where the anime actually preceded the manga. Is this the case? 

P.S.: I know that there are several anime without a manga. I also know that there are manga created from games. That's not what I'm asking. I'm asking whether or not there is a series where the anime came before the manga.
Yes, there are exceptions to the "rule" that an anime must be inspired by a manga. There are indeed some anime that do not have a manga corresponding, and other such things.

But yes, there are also anime series which inspired one or more manga.

The following list are some of the (arbitrarily selected as recognizable) names from a more complete list featured on the TVTropes article "Anime First":


Code Geass
Cowboy Bebop
Digimon Xros Wars
Nausicaä of the Valley of the Wind (as the article says, a weird example; the manga was created for the purpose of guiding the anime film)
Wolf's Rain