Vote: No, and never will.
Granted, the "never will" part is kinda up in the air. I have no intentions of installing Origin, but that doesn't mean that I won't be forced into it at some point by a game that I really, really want to play. So the "never will" part is only really applicable to the forseeable future.
And no, it's not because I'm a hardcore fan of Steam. I have Steam, don't get me wrong, but I'm not as obsessed with it as some seem to be. I for one hate digital distribution of games, or movies and music too for that matter. I like to have a hard copy in my hands. I've bought digital copies of games in the past, sure... some of those 50% to 90% off sales on Steam are hard to resist when it comes to a game that I'm somewhat interested in but wouldn't be likely to buy under normal circumstances. But the point is that I already have Steam. I don't need two programs to give me the same service that I rarely take advantage of anyway. If Origin had come along first, I'd probably be saying the same thing about Steam right now.
That said, I do admit that I'm additionally put off a little bit toward Origin because of Electronic Arts. Those guys have changed a lot over the years, and have strayed very far from their humble mission statement. At one point many years ago I felt like, as an avid gamer, I was more than just a statistic to them. These days... not so much. I'm not really angry with them... I'm not going to be one of those people raging for a boycott of EA titles... I think I'm mostly just... disappointed. I guess that's the word.