Phantasy Star III - Was probably the worst of the series as far as storyline, and character growth, but was the first RPG I really got into and played to the end. My mother bought this for me at a place called Software Etc during a random visit to our local Mall. It was in the bargain bin for $14.99. I had to agree to not ask for anything else for awhile, and not gripe when it came to chores. As straight forward as any RPG of its time. You'd recruit people for a common goal to kill some boss terrorizing the land, and then would have a choice of two women to marry at the end of each generation. Depending on who you chose, you'd get any number of characters and storylines. Two faithful cyborgs were by your side the entire trip. I can't say I'll ever go back and play this again, but my heart holds a fond place for this game as it introduced me to RPGs, and it kept me busy while I saved up money for FF6, and a SNES.
Final Fantasy VI - I can't say enough about this game. I'm one of those old guys who rants and raves about this one. If PSIII was the first RPG I played start to finish, FFVI was the first I completed. My first glance into this game was at my friend's house for a sleepover. He had just gotten it and was only a few hours into the initial scenario split from the Returner's meeting. I was immediately hooked. I guess you can say this was the reason I purchased PSIII. My first play through was 60+ hours. There wasn't a part of the map I didn't investigate. I bought gaming magazines that had tips & tricks, game art, whatever I could fine. Every year I still play this game at least once.
Chrono Trigger - This was the first game I had ever anticipated. I never really was an avid gamer until I bought a SNES. I started seeing advertisements in magazines for this new "Squaresoft" game coming out. Much like PSIII, I found this game and begged my mom to buy it for me as a Christmas gift. If she bought me that game, I wouldn't ask for anyone else. I meant it, too. She reluctantly agreed, and sure enough, it was my main gift, though, I did get other things. Sadly, I wasn't the perfect son as I located where she hid the game and put about 4 hours into it before feeling guilty and putting it back...after deleting my save. I don't go back and play CT as much as FFVI, but I do revisit it often. Most recently last year. I've seen every ending, and all of the extra cutscenes you can setup. SEE: Saving Lucca's mom. This will forever be in my top 2 games of all time. Chrono Trigger, and Final Fantasy VI helped me through some dark middle school times of my life. I wasn't a tragically bullied kid, and had a wonderful home life, but these games allowed for me an escape.
The Legend of Zelda - I never have beaten this game, and to be honest, I watched my brother play this far more than I ever will. My first gaming system was a NES. I couldn't tell you how excited my 8-year old self was whenever I saw this unwrapped. I had my very own NES...I just didn't have a TV. So I either played this on the livingroom tv, which was normally kicked off by my sister, or my brother's tv, which was normally him playing. I watched him play this from start to finish. Witnessing every battle, every boss, and seeing Ganon vanquished. The final dungeons music still creeps me out. I can't think back on my childhood and not think of my brother playing this.
Sonic the Hedgehog - If I could go back, I would have asked for an SNES rather than a Genesis. Of course, I can't say I didn't enjoy the crap out of Sonic the Hedgehog. Sonic was the first side-scroller I had ever beaten. And beaten. And beaten. I only had about six games for Genesis and they were mostly sports games. So Sonic was something I could zone out into and play for hours. He was the mascot for Sega, and went head to head with Mario for a time.
Honorable Mentions - Joe Montana's Sports Talk Football, The Legend of Zelda: A Link to the Past, Final Fantasy 7, Final Fantasy 8, Xenogears.
FF7, FF8, and Xenogears could have easily been on my list, but the ones listed were responsible for directing me to these games.