I think that it is hard for people to get into anime, but the same could be said about any form of entertainment. Anime in that sense is no different. Yet, it somehow turns people off, even if the subject matter is something that they would enjoy.
That is why I am careful when I introduce somebody to anime.
Because . . . .
There is no "best" anime we can recommend with so little information.
As I have already said, it depends entirely on the person's taste.
Also on their age plays a role in how the whole expereince goes.
Chances are they're not going to be happy if you introduce them to anime with something like Berserk or Ninja Scroll. (Try instead: Wolf Children or Mother's Day.)
A lot of people trying to introduce others to anime make the mistake of trying to push what they are interested in instead of considering what they person they are trying to introduce it to is interested in.
You might be able to introduce them to anime, but that doesn't mean they'll ever have any interest in watching the same stuff you enjoy either. Different people like to watch different things and that is okay.
Anime is not a genre, it's a medium.
There's bound to be something that would probably interest them if they actually bothered to sit down with it.
If you want to start with something "familiar" I would try Cowboy Bebop, the reason is simple, it is the most Western of the good anime series and can be a good starting point.
Some other good introductory films/series:
- Natsume Yuujinchou
- Fune wo Amu
- Usagi Drop
- Shouwa Genroku Rakugo Shinjuu
- Anything Ghibli