I eat alone on an almost daily basis. I have lunch by myself everyday at work and I love it. Gives me a chance to chill out in the middle I a work day and read my book for an hour. Right now I work in a hospital so going down to the cafeteria by myself isn't so weird, but at my last job I would go wherever I wanted for lunch by myself, and some paces were a little more upscale than TGI Fridays. I never sit at the bar because I like the room to lay my book down on the table. I try to tip well because I know a larger party could be using the table, and I don't want the waitress to feel they are getting shafted. My husband doesn't get off work until ten at night and sometimes, when I'm really craving something in particular, I'll stop at a restaurant for dinner by myself, too.
I have been to the movies by myself a few times. The first time was to get away from an overly annoying roommate. The other times were because I wanted to see a movie I knew my other half wasn't interested in and he was working or otherwise busy.
Having said that, I Ike the idea of a service that will match you up with other people to have lunch with because I personally have no idea how to find women to be friends with when I'm not working or in a class with them.