I can recommend Baccano to just about anyone provided they don't mind blood and gore. (It's funny, exciting, clever, well-written, and has great characters. It's also not nearly as gory as Elfen Lied). Cowboy Bebop and Trigun also helped me get into anime, as did Full Metal Alchemist. Be warned about Baccano though, the first episode is extremely confusing. Ghost in the Shell is more for hardcore sci-fi lovers, but it's still a great classic and I know a lot of people who have gotten into anime because of it. Ouran High School Host Club is a good comedy (I don't personally like it but I know lots of people who do, especially girls). Vision of Escaflowne, Moribito, and 12 Kingdoms also have classic fantasy feels to them, if that's the sort of thing you're into. Black Lagoon is also a good one to help ease into anime as it appeals to a lot of Western audiences, but again, you have to be okay with violence and swearing. If you want something sophisticated and thought-provoking, definitely check out Kino's Journey and Wolf's Rain.