There's just... so many...
But I guess I'll do a handful.
Firstly, every single JoJo opening is amazingly well animated and directed. Almost every one of them is steeped in subtle (and sometimes not-so-subtle) foreshadowing and symbolism, or builds itself as the show progresses. A lot of them also have some really cool changes when approaching the climax of each major story arc that range from the addition of sound effects to some sort of nod to the antagonist's ability.
Also the songs that are attached to them are stylish, bombastic, and kick-ass (as they well should be).
Bok already covered Steins;Gate.
Spice and Wolf's first opening has some really strong direction going for it too. It does a good job with it's transitions, for example the transition from the bag of wheat, to the coin rolling on the table, to the wagon rolling across the countryside signifies the relationship between the two protagonists. Naturally, I'm not an expert on film, or analysis by any means, and I'm totally getting this stuff from a guy on Youtube with the channel name "Mother's Basement" who actually is, go check him out if you feel inclined.
The song is very tranquil and fits the series' prevalent theme of traveling exceptionally well (and indeed, the song's title is
Tabi no Tochuu, which translates as "On a Journey", with like-wise fitting lyrics).
In Gatchaman Crowds' second season opening,
insight, I absolutely love the use of cardboard cutouts of the characters in a real world setting to represent motion, plus the visuals and song are pretty great too.
Baccano's opening is also pretty swell. Check it out if you like cool jazzy music attached to a cool jazzy series.
It's Always Sunny in Philadelphia's intro never fails to make me laugh.
There's plenty of others, but these are ones that exist. Might add more later if I think of any that I really feel the need to talk about.