First opening spoiled Chad and Ishida joining the group, as well as their powers.
Second opening spoiled that Hanatarou would join the group, Ichigo's oncoming fight with Kenpachi, and Renji and Ichigo's fight. However, this opening had tons of Bait-and-Switch Credits, like Ishida fighting Hitsugaya, and Yoruichi fighting Soifon while in cat form. It had so much fake stuff that you can't pick out the real parts until after you've already seen them anyway.
How does it spoil Aizen being alive? He's shown for about three seconds, and from the angle all you can make out is his hair and captain's haori. And it's shown during the beginning part, which goes through every one of the ryoka and Gotei 13. It's so subtle that you're only going to notice it if you're looking for it, especially with all the emphasis it puts on making Gin look creepy and evil.
The fifth opening shows several fights from the Arrancar arc (although you have to look very closely), as well as Ichigo fighting his inner hollow.
The opening for the Arrancar arc (Opening 6) spoiled that Orihime will be kidnapped by Aizen. Well in advance of the actual event, and by the time Orihime's abduction actually occurs, the opening has changed again.
It also shows the remaining Espada beyond Ulquiorra, Yammy and Grimmjow a good number of episodes in advance of their actual introductions.
The one after that spoiled that Renji and Rukia would join the Hueco Mundo force.
And the 9th opening, following the filler arc spoils the four captains coming to the rescue in Hueco Mundo, as well as Nel's true form, and spoils them hard◊.
Let's not forget the spoiler endings. Ending 10 spoiled Ichigo's father being a Shinigami—a Captain, no less and another showed the Vizard's previous appearance, several episodes before the Turn Back the Pendulum arc began.
The third ending is especially guilty, showing Ukitake and Kyoraku as Yamamoto's students, Urahara being Captain of Squad 12, and Gin and Rangiku's prior relationship.
The broadcast version of the 13th ending on Adult Swim (which typically shows random shots of the season set to an abridged version of the ending theme) shows a shot of Aaroniero with his mask off while he is impersonating Kaien.
The 12th opening (after the end of the Muramasa/Sword Fiend filler) manages to spoil an incredible number of things, including both of Ulquiorra's Ressurecions, Starrk and Barragan's Ressureccions, Ichigo's super-hollow form, Soi Fon's Bankai, Wonderwiess's appearance, the Vaizard's appearance, and even Kensei's bankai, and, most importantly, The Heart Granted, some of this could be guessed, but if one hasn't read the manga this opening essentially spoils about half of the awesome reveals in the FKT arc.
The thirteenth OP spoils Isshin, Urahara and Yoruichi joining the battle at FKT, Ichigo's jinzen training in the Dangai and Gin's death. Considering the latter two won't be animated for months and the latter unconfirmed until the latest chapter of the manga those are some pretty big spoilers. It also very subtly spoils Ichigo's loss of powers, with the scenes from beginning of the anime played backwards as a hint that Ichigo will revert to state before them. But this is almost impossible to figure out without reading last chapter of the manga.
It's almost a theme to Bleach at this point that the openings preview(/spoil) upcoming events, and the endings tend to focus on the past. There are exceptions of course.
Just when we thought they couldn't outdo themselves, they did: the latest filler arc opening shows the various captains of the Gotei 13 fighting one another, and the mysterious green-haired girl who has just been introudced. And to add insult to injury - at least in terms of spoilers - the latest ending shows Mugetsu Ichigo, his Bankai mask cracking, and various shots of Ishida, all of which serve as a subtle hint at the manga's development of Ishida becoming the new Hollow-slayer - this arc is established as taking place between Aizen's defeat and the manga's current storyline.
The 15th Opening seems to have no problem with showcasing Ichigo and Ginjo's Fullbring, Ginjo standing alongside Ichigo's friends and Tsukishima's face along with Ichigo and Ginjo vs Tsukishima and Shishigawara despite all of those being spoilers, those last three especially, seeing as how the viewer is supposed to think Ginjo is the new Big Bad, we don't see Tsukishima's face in the manga until he attacks Orihime which wasn't animated until a good few episodes later.
And after the episode animating Rukia's return, the ending is revised to show Ichigo's upgraded Shinigami outfit, followed by the new looks for Rukia, Renji, Byakuya, Hitsugaya, Kenpachi and Ikkaku.