I am a big fighting game fan and I downloaded Skullgirls just because I love the genre. The graphics and anime style is not to my liking, but this game has one of the best fighting game tutorials after Killer Instinct. Just completing the tutorials to both these games will bring any newbie into the fighting game scene without much hassle.
Skullgirls has great mechanics, simple execution, and a very friendly playstyle so even newbies can easily get into the game. Totally a must play.