The '02 and '14 seasons are obvious choices. I'll pick some that don't get enough credit.
2005: Despite losing the heartbreakers to Texas and Penn State, the second half of that season was awesome. From the infamous John L. Smith meltdown after the blocked field goal against Sparty to the Gonzo catch against Michigan, and of course the bowl game against Notre Dame. I know the '06 team had a better year, but the '05 team, in my opinion, was the most talented this century.
2009: Much like 2005, they had a heartbreaker against USC, then a complete meltdown against Purdue. But after the Purdue loss, all seemed smooth. From exacting vengeance on the Nittany Lions, to the OT win against Iowa to clinch the Rose Bowl, and the win in Ann Arbor. Then to top it all off, they end the three-year winless bowl drought by beating an Oregon team that was supposedly too fast for them. Add on that Terrelle Pryor looked like a legitimate Heisman contender for the upcoming 2010 season, and there were several reasons to be optimistic.
2010: Yeah, all the tattoo and selling memorabilia crap happened, but that team still went 12-1 (fuck off NCAA, I watched every game with my own eyes. They happened), blew out Penn State and Michigan, vanquished Iowa and their pink locker rooms in dramatic fashion, and finally beat an SEC team in a bowl game. None of us knew it at the time, but it was Tressel's last year. In hindsight, you enjoy it more than you did in the moment.