http://myanimelist.net/animelist/Chrono1219&show=0&order=4
Any show within the 9/10 realm is a really good starter choice.
However, as usual I tend to try to get people to watch some of the classics from the 90s early 00s before they delve into the more modern things. Classics like Cowboy Bebop and so on. Even some shows that might not have 9s or 10s (GTO, Outlaw Star, Evangelion) on my list I'd consider to be must watches.
If you really want to jump right into stuff that has aired fairly recently then obvious choices like TTGL, Baccano! and Fullmetal Alchemist: brotherhood are very good and it's hard to find people who don't enjoy them. The most recent anime that really blew me away is Steins;Gate which just finished airing last season.
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Chrono1219