One of my favorites of the Smithsonians is the Museum of Natural History, where boyfriend and I took a ramble a few weeks ago. Most of the museum is full of dead things, but there are few living items as well. I think it's a yearly thing, but they occasionally have an orchid exhibit, which is really amazing. Boyfriend and I got took some time to smell the orchids and learn a bit, as we wanted to head out to an orchid store in the boonies of Virginia to stock up on orchids for terrariums. Al's Orchid Greenhouse is amazing, and Al is quite the character himself. He went through the greenhouse with us and told us about every orchid that could possibly be used in a terrarium, and we came home with a nice selection.
Another exhibit at the museum that I like (which I think is a permanent exhibit) is the Orkin Insect Exhibit. I'm not sure how I feel about Orkin sponsoring it, but it's pretty neat. I liked the display window full of moth and butterfly chrysalises. I was able to sit there and watch one hatch.