Must see things in Frankfurt, Dresden, and Berlin?

If you're in control of how much time you spend in each city, consider giving more to Berlin and less to Frankfurt. Berlin is sprawling, teeming with arts and culture and events and various interesting neighborhoods, whereas Frankfurt is much smaller in terms of culture and things to see (notice how the answers above are mentioning daytrips when they talk about Frankfurt?). Dresden is in the middle: less touristy and interesting to explore but not as 'full' as Berlin.

Thanks for all the suggestions everyone, the trip went well. I saw the Pergamon, zoo, art gallery, check-point charlie, and the Reichstag in Berlin. The communications museum (where a robot arm drew a portrait of me), film museum, and art museum in Frankfurt with a daytrip to picturesque Heidelberg. Not bad for six days and having a severe cold the whole time.

I recommend visiting the Swinger museum in Dresden. It is a collection of museums featuring fine art, weaponry, science, and more. Nearby Dresden is the porcelain factory at Meissen. Meissen was the first porcelain factory outside of China, and is considered the finest western china.

The Berlin walking tours offered by http://www.berlinwalks.com/. Dunno 'bout the others but their "Infamous Thiord Reich Sites" was quite memorable and interesting.

The Checkpoint Charlie Museum was probably one of my favourite things I saw in Berlin. But if you can get to Oranienburg (just outside of Berlin), Sachsenhausen Concentration Camp is a truly sobering and educational experience.

In Berlin, the Brecht house (be sure to eat at the restaurant too), http://www.gruenderzeitmuseum.de/htm/index_engl.htm (call in advance for an English tour and the http://www.dhm.de/museen/kollwitz/english/home.htm museum.

Berlin is one of the most interesting big-cities I've ever been to, and I will also suggest putting a bit more of your time there. In Berlin: Thirding Tacheles, the artist-collective-feeling, run-down building off Oranienburgerstrasse. You'll know it when you see it. There is a different bar on every floor, and a small but neat little artist shop about halfway up the building. Nthing going to the top of the Reichstag, where you can get great panoramic views of Berlin for free. I went about an hour before closing and didn't have too tremendous of a wait (plus got a sunset sky). And if you are going sometime in the next few weeks, you will undoubtedly run into more Weihnachtsmaerkte than you can handle. Try Gluehwein and/or Feuerzangenbowle.

In Berlin: The Soviet Memorial in Treptower Park is built from pieces of the Hitler bunker. Little fact. Berggruen is indeed a fine collection. It has nothing to do with Berlin or Germany in any way, it's just a huge bunch of Picassos, Klees, et al. Hamburger Bahnhof is an interesting modern art collection in an interesting building. EnormousTalkingOnion: you're probably thinking of http://super.tacheles.de/cms/, it was an artists' squat that successfully made itself legitimate. I don't like it, it's purely a tourist money-making scheme, but if you're interested in the history of squatting it might be good to see. If you like architecture, then go to the Reichstag and walk around there a while...that's the government district, the 'Regierungsviertel', and has lots of good buildings...and then take a walk down to Potsdamer Platz, which is arguably ugly as fuck but quite a spectacle one way or the other. Max and Moritz is indeed a good German restaurant at the beginning of Kreuzberg, which is in and of itself an interesting district.

If you like minimalism, you should go to the http://www.hamburgerbahnhof.de/cont/conte/ in Berlin.