I've got a few picks. They're the same ones I suggested to my friends.
Deadman Wonderland (Very enjoyable. It has a story that can appeal to pretty much anyone. I'd suggest this to anyone who I know likes action and gore.)
Code Geass (Not as easy to follow, but it too is very enjoyable. Again, I feel like it doesn't take a specific person to like it.)
Golden Time (This is one I'd be much more likely to suggest to a girl. It was my first anime, but I highly doubt most of my guy friends are a fan of romance. It's easy to watch, and can be a good introduction to anime cliche, etc. Not too offputting.)
Sword Art Online (Don't lynch me plz. I know that it's pretty much the laughing stock off the community, however, it's one of the most known shows for a reason. People make fun of it because it's so mainstream, and it's easily related to those who watch like 5 series then call them self otaku, but, that's for a reason. Even though it has a lot of flaws, it's easy to enjoy.)
It sucks, there are so many shows that I enjoy much, much more than these, but I know that they'd probably be offputting to a newbie.