We know space is big, but trying to understand how big is tricky. Say you stare up at the sky and identify stars and constellations in a virtual planetarium, you can't quite fathom how far away all those stars are (previously, twice). Even if you could change your point of view and zoom around in space to really see 100,000 nearby stars (autoplaying ambient music, and there are actually 119,617 stars mapped in 3D space), it's still difficult to get a sense of scale. There's this static image of various items mapped on a log scale from XKCD (previously), and an interactive horizontal journey down from the sun to the heliosphere with OMG Space (previously). You can get a bit more dynamic with this interactive Scale of the Universe webpage (also available in with some variants, if you want the sequel [ previously, twice], the swirly, gravity-optional version that takes some time to load, and the wrong version [previously]), but that's just for the scale of objects, not of space itself. If you want to get spaced out, imagine if If the Moon Were Only 1 Pixel, and travel from there (previously). This past March, BBC Future put out a really big infographic, which also takes a moment to load, but then you can see all sorts of things, from the surface of Earth out to the edge of our solar system.
100,000 Stars [SLInteractive3DVisualization] (Seems to run best on Chrome or Safari and a decent graphics card)
Visualization of the dark matter in 1/1000 of the gigantic Bolshoi cosmological simulation, zooming in on a region centered on the dark matter halo of a very large cluster of galaxies. ... The Bolshoi simulation is the most accurate cosmological simulation of the evolution of the large-scale structure of the universe yet made (“bolshoi” is the Russian word for “great” or “grand”). (The Formation of the Milky Way and its Neighbors is cool too.)
Asteroid Discovery From 1980 - 2010: an animation of the solar system that highlights asteroids as they are discovered. I would suggest watching it in a high resolution.
The Anatomy of Spiral Arms, shows how galaxies naturally evolve to form grand-design two-arm spirals. The Hubble Ultra Deep Field in 3D. [more inside]