I never joined, but was seriously investigating the church earlier in my life (see http://exmormon.org/phorum/read.php?2,1131036). Apparently, I was added to the rolls as a member by an enthusiastic official. My wife asked to have me removed when she learned of it. My 2 questions are:
1. Does it matter? I don't know if I'm on the rolls or not. What does it mean if I am?
2. Should I care? I don't really care. I'm sure I'm on a number of lists I have never signed up for.

I used to be a ward clerk, but I have no idea what would be involved in having a non-member on your rolls. I've never heard of it being done. I know some non-members have been given callings, but I always thought they were off-the-books affairs.

I do know that the immediate family of members are (sort of) kept track of in the church records, even if they're not members. In your case, on your wife's records, there will be some information listed about her husband. I don't remember exactly what information they keep, but your name, at least, is in their system. But you shouldn't be listed as a member if you were never baptized (there's a bit of paperwork involved in adding a new member, some errant clerk can't just do it by accident). I would assume that, as a non-member, you wouldn't be on the rolls of any ward, but I don't know. Stranger things have happened in the Morg.

Does it matter? That depends

http://exmormon.org/phorum/read.php?2,1130715,1131030#msg-1131030

on whether the "church" now has a legal hook into you.

Some folks believe that there is a US law that says the "church" can now do with you as it will.

If no law, doesn't matter.

I'd call the ward clerk or SLC Member records and ask if you are listed as a member. If you were never baptized, then you could demand a copy of your baptismal certificate, and could have a forgery complaint. That'd be entertaining, and could get you an out of court settlement. Of course, it would take time and aggravation to investigate that.

Or you could just resign, and if you are not a member, they would tell you that.