Maquoketa Caves, Maquoketa- One of my favorites. It's a great wilderness area with tolerable camping facilities and, oh yeah, caves. There's just something about being underground like that, and it's not just the thought of all of the earth above crashing down on you. 
The Ledges State Park, Boone- A random valley in the middle of cornfields, this niche of a park is refreshing. The sharp horseshoe valleys guard a nice ultimate frisbee area and offers other nice hiking. Avoid: crossing the creek crossing when a car is near- they may speed up unnecessarily and drench you.
Backbone State Park, Strawberry Point- I vaguely remember very cool hiking trails in some sweet hills, a very cold wading creek (in which dad killed a mondo crawdad), and a cool camping experience. Apparently good trout fishing?
Lake Red Rock, Pella- Surrounding this lake are several state parks with nice views, including one from the top of the observatory. There are some friendly-sized cliffs for free climbing. 
Botanical Gardens, Des Moines- I could live here, except it costs like $8 to get in the doors. Even though Iowa heat and humidity are killers, the rainforest environment is great. The abundant foliage is fun to escape into, a little bit different than getting lost in a corn field. 
The fish add to the living jungle aura, as did the birds and lizards (I haven't seen them the past few times).
Old Threshers, Mt. Pleasant- I must objectively admit that it is a sight worth seeing. I must stress, though, that it's novelty only lasts so long. This is primarily a festival celebrating...antique threshing machines. Recommend:Log village and sarsaparilla, gunfight at the North Village and on the train, food, ubiquitous yard sales :).
The Capitol Building, Des Moines- I've heard it's quite grand in comparison to other state capitols (personally unverified) and in proportion to the grandeur of our state. It is quite a piece of old architecture and a stunning mass of gold. There's an especially cool-looking library (not actually cool- only law books). And one can go all the way to the top of the dome via narrow winding stairs.
Old Capitol, Iowa City- I'm sure it's as good as I remember, even with the fire that partially damaged it recently. Iowa's first state capitol building (though third territorial) now holds a pretty neat historical museum. Also, there is a sweet (to me, at least) museum next door with an enormous collection of wildlife specimens.
Covered Bridges (of Madison County), Winterset- made famous from the movie Bridges of Madison County (this is not a recommendation of the movie). For as long as you want to look at covered bridges, they're there and worth seeing. Also, the county park has a nifty stone tower and hedge maze.
Amana Colonies, Amana- A quaint collection of preserved communities. I really only remember quilt shops and hating the sauerkraut.
Snake Alley, Burlington-(one of) the crookedest street(s) in the world, depending upon criteria and official verification (?). Anyway, quite fun to see and walk up (better walking down). A bright spot in Burlington and really close to the Salvation Army store, yes!
Iowa State Fair, Des Moines- An event that can engender indeed mixed emotions (pride to shame). Great food, unique atmosphere, tons of sweat, the authentic barnyard smell, etc. 
Dwarves was popularized by Tolkien.
Thanks to Arnold Zwicky via Abraham Piper.
