It depends on genre.
sci-fi: Stiens;gate or FMA: brother hood
sports: kuroko or haikyuu
drama: nagi no asukara
Usually Death Note, as it is a very good anime in and of itself, plus newcomers will want to watch stuff without subs and Death Note is one of the very very few dubbed anime that's actually pretty good.
Cowboy Bebop is a classic for a reason, but there are many recently that seem to tell me Hunter X Hunter was their start.
Honestly mine was Yu-Yu-Hakusho, Gundam Wing, and DBZ.
Soon after I watched Fooly Cooly and Wolf's Rain which pushed me passed the casual viewer line.
Naruto/Shippuden, Dragon Ball/Z/Super, Soul Eater, My Hero Academia, any of the Fate series, Tokyo Ghoul, Seven Deadly SIns, and my personal favorite Neon Genesis Evangelion