Final Fantasy VIII. I started it YEARS ago, but found the graphics distracting, the gameplay and levelling up system dull (I only enjoyed games like Spyro and Zelda), and the story slow. Then I purchased Final Fantasy X and loved it so much that IX, VII, I and II, and IV swiftly followed. I decided to resume VIII a few months later... and I loved it. It's now within my top 10 games, and only second to X in terms of the Final Fantasy series.
A few years prior to this, I had been unable to get into Zelda: Majora's Mask, and had decided that all Zelda games were not worth the effort. A year after this, I bought a Gamecube package which included Wind Waker (I was not too happy!). It took me a few weeks to open it, but when I did, I became hooked instantly. Wind Waker is now a top game too, and Majora's Mask is... alright.