F-SIM Space Shuttle price drop
Probably as close as you're going to get to actually flying one of these...
What better time for F-SIM Space Shuttle to do a price promotion than during Endeavour’s final flight into space. For budding astronauts it may not be quite the same as actually going into space, but it’s a decent simulator all the same. You can get it for 59p here for a limited time.

From the publisher: “F-SIM Space Shuttle is a highly realistic flight simulator. It simulates the Space Shuttle approach and landing in unprecedented detail and accuracy. Take command of the Orbiter during the final minutes of descent and safely touchdown at John F. Kennedy Space Center or Edwards Air Force Base. After touchdown, sophisticated landing analysis is available. Only the best pilots are awarded a “perfect landing” score, and even those can push their limits and put their skills to the ultimate test by adding wind, gusts, and turbulence or simulating system failures like a stuck speedbrake…”