For seeing the sights, look into either the Canadian Niagara Parks pass or the New York Niagara State Parks pass - you can end up saving money by buying the pass (even if you don't see everything included).
Must do's:
Maid of the Mist (or Hornblower now on the Canadian side) - they do exactly the same, so go with the one that is most cost effective with the pass.
Cave of the Winds (U.S. Side). It takes you under Bridal Falls and is really a blast.
Journey Behind the Falls (Canadian Side). It takes you behind the Horseshoe Falls and to a platform just to the side of the falls.
Spanish Aero Car (Canadian Side). It was built by the same company that built the Golden Gate Bridge. It goes over the Whirlpool.
Whirlpool Jet Boats (U.S. Side). Blast of a boat ride.
White Water Walk (Canadian Side). Nice path that runs along the Canadian side of the rapids.
Goat Island and the Three Sisters Islands (and Little Brother Island) (U.S. Side). Wonderful to walk around. You can walk right up to the river (PLEASE pay attention to the signs stating not to wade in the water - it may look peaceful, but many people have been pulled over the falls by doing just that).
Lots of other things to see depending on your interest. Historic sites, botanical gardens, butterfly conservatory, aviary, movies, carnival midway, etc.
P.S. In the movie Niagara, when he chases her at the falls, the shots were taken at different places (the tunnel part was from Journey Behind the Falls; the getting soaked in the falls was Cave of the Winds; etc.) It's kind of fun to watch the movie and try to identify all the locations.
Also, if you like to read a bit about where you're visiting, check out T.W. Kriner's In the Mad Water and Journeys to the Brink of Doom. Lots of stories of folks (and animals) going over the falls - both on purpose and accidentally.