I wish I could replay games more often than I do. The most time I had to replay games where those lovely middle school and high school years. As such, this is what i can remember playing:
FFV - I've beaten it 3 times now if you include the GBA game. I beat it once for fun, then I wrote my own walkthrough on the 'net the second time through (it was crap but it had screenshots to guide you), then again for FFV Advance.
FFVI - 4 times on this one. The first time I beat this, I had this weird glitch; when I went to get Gogo, one of those construction-worker-dudes kicked me off the bridge. In fact, he kicked me off the bridge a good half-dozen times. The last time it happened, I was SO angry that I mashed on my controller as I fell from one screen to the next. Then, I hit start to use potions/ethers (low hp/mp from the random encounters), and TADA! I had 99 of every item in the game, including the Paladin Shield, Ragnarok Sword, and whatnot. In Espers, I had Odin and Raiden simultaneously, which is supposed to be impossible. It was excellent. But I felt like it was cheating, so I beat it a second time that same year. Then there was the PSX remake. Ten years later, GBA port.
Chrono Trigger - Only fools didn't take the time to get ALL the endings. This took me three complete play-throughs instead of two, cuz I missed a few my second time around.
Alundra - Once by myself, once with a friend and my little brother...we had WAY too much fun with this game.
Star Ocean: The Second Story - Once with each protagonist in the lead. The first time I totally missed everything and got a crap ending. The second time I was on my way to the best ending, but I missed some trigger to get the last event with Chisato...it pissed me off.
Final Fantasy Adventure - I beat it once per summer for about...six summers in a row. It was my "family road trip" game.
Final Fantasy Legend II - Same as Adventure, but slightly less awesome for me. I probably beat it 3 times.
That's about it...except, more recently, I'd say I beat Ys: The Ark of Napishtim either 3 or 4 times and gotten really good at Time Attack.
I wish I had more time to play RPGs more than once, but as a devoted reviewer, I try and portion my time out evenly for as much stuff as I can. Currently, I can boast that I've beaten 101 RPGs...I won't stop until at least 200! :)
PS - Welcome. You sound hip.