The ending in Super Mario Galaxy 2

There are a total of 242 stars:

• 120 standard Gold stars, consisting of:
  • 56 Power stars (the normal ones)
  • 6 Grand Stars (at the end of each world)
  • 17 Hidden Stars (in 17 different galaxies)
  • 29 Comet Stars (in 29 different galaxies)
  • 6 Additional Normal Stars after beating the game for the first time.
  • 6 Additional Comet Stars after beating the game for the first time.
• 120 Green Stars which appear after you collected the first 120 yellow stars and have beaten the game again (2 or 3 per galaxy, 18 per world, except for the very last world, which has 12)
• 2 additional Gold stars after you have collected all the previous 240 stars. (1 Power Star, 1 Comet Star, which also requires 9999 Starbits)

The only way to get all Comet Stars, is to collect all Comet Coins, which are found on the first level of each galaxy, including the very last one!

Note that it is possible to get Bronze Stars instead of Gold Stars if you use the Cosmic Guide available (after dying a couple of times) on certain levels (available in every galaxy, but not every level). While these Bronze Stars allow you to continue to move on, the do not count with respect to unlocking certain secrets.

Here are the levels that are directly based on previous levels:

• Topman's Tower, in the Space Storm Galaxy, is based on part of Buoy Base Galaxy from Super Mario Galaxy.
• Throwback Galaxy is based on Whomp's Fortress from Super Mario 64.
• Mario Squared Galaxy is based on part of Toy Time Galaxy from Super Mario Galaxy.
• Twisty Trials Galaxy is based on The Secret of Ricco Tower mission in the Ricco Harbor level of Super Mario Sunshine.
• Stone Cyclone Galaxy is based on the Cyclone Stone mission in Beach Bowl Galaxy of Super Mario Galaxy.
• Boss Blitz Galaxy features five bosses from Super Mario Galaxy.

There are also some that are more loosely inspired by previous levels:

• Supermassive Galaxy is similar to Big Island from Super Mario Bros. 3.
• Flip-Swap Galaxy bears some resemblance to the Secret of the Dirty Lake mission in the Bianco Hills level of Super Mario Sunshine
• The Tall Trunk's Big Slide mission in Tall Trunk Galaxy is similar to slide levels in many 3D Mario games, and features a remix of the theme from Princess's Secret Slide from Super Mario 64.
• Starshine Beach Galaxy features many elements from Super Mario Sunshine: Piantas inhabit on the island, there is a statue similar to the one from Delfino Plaza, the island is slightly dolphin-shaped, and even the name "starshine" seems to be a reference to "sunshine".
• The Gearmo challenges in Rightside Down Galaxy and Upside Dizzy Galaxy are similar to the Gearmo challenges in Battlerock Galaxy and Dreadnought Galaxy from Super Mario Galaxy. (In the first game, you cleaned up trash by throwing Bob-Ombs; in the second game, you use a fire flower.)
• Honeyhop Galaxy features many elements similar to Honeyhive Galaxy from Super Mario Galaxy, but the level geometry is actually quite different.

_{I'm marking this community wiki. Feel free to add to this answer!}