My name is Jennifer and I am a recovered ride weenie!
Seriously, I spent my life HATING "big rides" after having a panic attack on a kiddie coaster when I was, well, a kiddie. I am uncomfortable with heights, and thought (swore) I would NEVER do Splash, or BTMRR, or Space, or even Goofy's Barnstormer!
But all that changed.
Once (two years ago?) when we were making our WDW plans and listing our "musts," my DS said, "my only 'must,' my only wish for this trip is that mama tries Splash Mountain because I know she will love it." Uh, honey? Are you sure you don't want to wish for something else?
OK -- so, long story short: what I learned is that (1) it really does make a difference to your family if you are the only one always sitting things out, (2) if you relax your body instead of tensing up every muscle, it makes a huge (pleasant!) difference, (3) it is possible to take baby steps and build yourself up and (4) even if you hate it, it doesn't last long.
BUT -- I don't hate it any more!! I LOVE BTMRR and can assure you it is NOT really like a roller coaster at all (no mega drops or anything). I advise trying and deciding that you can deal with Goofy's Barnstormer because in some ways I think that's actually worse than BTMRR. Can you handle Test Track? Then you can do BTMRR (and Test Track is another good introduction). As others have said, Splash is a tremendous ride even before you get to the drop and if you just relax your body and breath deeply then it's over before you realize it. I've even tried Space Mountain. I didn't like it, but it didn't do me any harm and I'm proud that I've got it under my belt.
Will I ever do EE? Probably not. But I have exponentially more fun at WDW now that I'm willing to try and enjoy more rides.