I don't find the Rays boring, but I do find them un-entertaining. Awesome pitchers but a plinky offense. Part of it is also the basement apartment vibe I get from watching their home games and the sub-minor league attendance numbers. It's all so drab.
Boring, for me, is a team with mostly mediocre pitching and a middling offense. So, the Twins (this year).
The Red Sox, as much as I hate them, are not boring. They're a pretty exciting team who had some things go wrong for them this year. Red Sox tears are also like sweet wine to me, so watching them implode is almost more fun than my heart can handle.
I really find the White Sox boring too, but they've got some good pitching pieces and watching a guy like Chris Sale carve up an opposing lineup is never not fun. Same goes for the Mariners and Felix, but I'd rather choke to death than watch their lineup (Cruz and sons).