> It's not the length of a day that will impact Mars-dwellers the most, it will be their internet speed.
No, it'll be their latency. I believe the scenario informally tossed around by IETF for "extraterrestrial internet" envisions three categories of latency... a relatively small amount of net bandwidth sent directly between Mars and Earth that enjoys the lowest possible latency, and two roughly equal amounts of bulk bandwidth with much longer latencies. handled by satellites at the L3, L4, and L5 Earth-Sun and Mars-Sun Lagrange points. For semi-adhoc websurfing, your request would get sent along the fast (bandwidth-limited) link, and the response would travel along one or both of the lagrange paths. Someone like Akamai would come up with an open web standard that allowed sites to export themselves in their entirety (and remain synchronized in an rsync-like manner) so they'd run in a local VM on Mars.
Let's use StackOverflow as an example. To kick the whole thing off, SO would take a snapshot of itself (kind of like it already does for archive.org) and begin uploading it to the server on Mars along the high-latency longer lagrangian bulk-data path. Once the server on Mars had a complete copy, it would become their local mirror. Normal bulk updates would occur frequently and periodically along the longest lagrangian path. Posted questions by someone on Mars (and the text of replies to them) might get expedited and sent along the shorter direct route.
Porn sites and Youtube would do the same thing. If a Martian wanted to visit some smaller site, he'd have to tag them for fetching and wait a few hours for them to become available. They'd probably follow a "Martians Pay" pricing model that split the bandwidth costs among everyone on Mars who accessed specific sites on a regular basis. Popular sites with lots of users (like Reddit and StackOverflow) would be cheap despite having lots of data because the cost would be divided among lots of Martian users. More offbeat sites might force individual users to be somewhat selective and conservative about their bulk-fetches (or at least about keeping them updated in perpetuity if they're only interested in viewing them as a one-shot activity), and might rebate back part of the initial acquisition cost if/when future users go to view the same site (ie, you, the first user, might pay $5 to bulk-grab all the blogger.com postings of {some-user}, but get $2 of it rebated back when/if some future person pays $3, and you'd both get another buck (and further diminishing rebates) as more people paid diminishing prices to gain access to it.
By the same token, cable networks like HBO and SkyTV would bundle their new video content daily and bulk-upload it to their local affiliate on Mars (who'd make it initially available at some official scheduled time, and thereafter by streaming).
Ironically, the biggest single limiting factor to bandwidth wouldn't be between Earth and Mars, but between the surface of the Earth and a satellite orbiting the earth in geostationary orbit.Between the L3 and L4 satellites, you can use 30GHz of spectrum if you've got the hardware & power budget to do it. Then double it by sending half the data along the path in the other direction. The problem is the "last mile" between orbit and the surface, where it's likely that something more exotic will be required (say, multiple satellites using tightly-focused lasers to ferry the bulk data between earth and orbit, then bulk-uploading their chunks directly to the lagrangian satellites.
In short, the future of interplanetary internet can be summed up as multipath, multilink, and Akamai-like CDNs hosting VMs for earth websites on Mars. The biggest hard challenges aren't the technical ones... it'll be dealing with Hollywood lawyers and the copyright mafia losing sleep at night that their precious content is being cached on Mars with insufficient DRM or that someone, somewhere on Mars, is listening to a song that was improperly licensed.
The resources to maintain this kind of large-scale local cache would be substantial... but probably agreed to without hesitation on the grounds that they'd be likely to make the single biggest difference to morale on Mars than anything not directly related to life-or-death.