TCP is already out as a protocol for our galactic internet, see relevant comment from Linux TCP implementation:

    /*
     * [...] Note that 120 sec is defined in the protocol as the maximum
     * possible RTT.  I guess we'll have to use something other than TCP
     * to talk to the University of Mars.
     * PAWS allows us longer timeouts and large windows, so once implemented
     * ftp to mars will work nicely.
     */

(This is from /usr/src/linux/net/inet/tcp.c)

This is correct. At their furthest apart, Mars and Earth are 22 light minutes apart. Their closest is almost exactly 3 light minutes. For comparison, the Earth and Moon are just over 1 light second apart.

On a more serious note, could tcp.c just be patched on the client to drop packets after ~10sec?

I sincerely hope ftp is a distant memory by the time the University of Mars opens.

well, why not? Martian students will need to use something to transfer files. Perhaps SFTP?

The International Space Station still uses Kermit! At least they did in 2003:

http://www.spacedaily.com/news/iss-03zq.html

Unsurprisingly, this is a well-known problem: http://ipnpr.jpl.nasa.gov/index.cfm

While I don't know that we can fairly say the Internet qua Internet has been extended past Earth (and associated environs), NASA certainly uses a Solar System-scale network already, and while they haven't made a big deal about some of the routing they've already done, if you read the press releases carefully they'll sometimes mention how they routed the signal from one probe through another. It's already a network.

I would encourage you all to look at the site dtnrg.org It's for the DTN research group, which among other things is beginning to architect and implement the so-called Interplanetary Internet. Some early trials have been run among NASA, ESA, and JAXA mission-control centers, as well as one flight test on EPOXI (used to be the Deep Impact mission)