People love the internet. Especially astronauts. You can get all kinds of practical information, keep in touch with family, and there are countless amusements for the boring parts. Just one problem: It's hard to get off-planet. It's really hard in high earth orbit, and past about the moon or so, just plain outright impossible. TCP/IP, the backbone of the internet, would literally time out before signals could reach, say, Mars, even when Mars is at its closest. To say nothing of the return trip. My Mars base is ruined!
NASA does have a solution that they call DTN, which they use in the space station and other orbital places. DTN has a much much much longer timeout. If you're patient, you could run signals as far as you need to. And this gives me an idea.
A DTN over radio link connects a caching computer to the Internet...by downloading all the pages it can get a hold of, transferring email, and uploading new pages and transmissions (such as, say, blog posts), and storing this. It would transmit once per day. Space stations or other planets now receive the internet via the caching computer. Admittedly, every page in it is, on average, a day old, but it is as it appeared on Earth yesterday, and it would work at area network speeds (100Mbs is cheap, and 10,000 Mbs is...available.)
This way, people in space can look up things on wikipedia, or write blog posts, or upload the Mars vacation photographs to their blog. From their perspective, the Internet just doesn't update very often, but it still works. And back on Earth, you might get notification late, but you will get it. It's the best I can think of without, you know, altering the speed of light.