Bleach, Dragonball, Hack Sign, S-cry-ed, Street Fighter(The Cartoon Movie), Shaman King, The Boondocks(Drawings are in an Anime style but is US product so it called a cartoon.), Akira(Ending scene is the only weird part), Neo Genesis, Pokemon, Yu-gi-oh are safer more mainstream Animes.
For crazy but more fun animes, ask these peoples! You must give them an offering first tho.