Since I can't say 'Dodgers' for this one, my most hated team is Atlanta. It's not been as fun to hate them lately since they've been so god-awful, though. It began in 1993 when San Francisco won 103 games and missed the playoffs because Atlanta had won 104. We have that situation to thank for the wild card games of today. I hated Chipper Jones SO much (for no real reason, other than he was the focal point of their attention). I hate the war chant and chop (reasons I also hate FSU). And I hated how by the end of two decades of nearly continued divisional domination, they regularly had upwards of 10,000 empty seats in their stadium for first round playoff games.
Winning breeds contempt, so I get that the Giants are now on people's hate radar, having won the WS in '10, '12, and '14. It's why I have hated the Braves, Yankees, Lakers, Bulls, Tiger Woods, and others over the years - not necessarily because of the winning itself, but because the winning caused the extreme over-saturation of media coverage, often at the expense of everybody else (especially back when your only national sports outlet was ESPN).