A few tests on the Singularity test server showed that a Crow Interceptor with a standard 8AU/s warp speed takes approximately 35 seconds to warp across this distance, jump through to the next system and be ready for the next warp.
So my chosen 96-jump route from 3KNA-N in Branch to MVUO-F in Period Basis should take just under an hour (96 jumps x 35 seconds = 56 minutes).
Of course something slower and less agile would take significantly longer. The biggest sub-capital ships' standard warp speeds of 2AU/s and their much slower align and acceleration times would make the same journey take upwards of 6 hours. That is assuming the unlikely event that they didn't get caught up in some local colour.
Edit: In further support of the above approximation, it turns out a far more thorough blogger, in the form of Marlona Sky, has put in the required effort to actually fly these kinds of journeys. Read more about The Cancers of EVE Online: Teleportation at the Reversal of Fortune blog.
And Now For Something Completely Stupid
Why? Because it's there! Watch out for that pothole Pierre.
Perhaps it's because of the Winter Olympics, but I think it would be interesting to attempt to set some time-trial records along pre-set routes under specific conditions. For example: Tranquility only, verifiable run by stream/FRAPS etc, records held by ship class.
I can imagine that many attempts will be marked up as a 'Did Not Finish', but imagine the accolades that might come from being able to claim you hold the record for crossing New Eden in a battlecruiser - it didn't do Han Solo's rep any harm (even if he didn't really understand what a parsec is). I would imagine it would develop into an alliance-dominated event requiring Tour de France-like peloton required protect the lead pilot.
Maybe it'd make an interesting in-game event. Just a thought.
Back to the matter of answering the titular question, so if someone asks how long it takes to cross New Eden, are we happy that the answer is basically, 'about an hour if you're lucky, longer if you're lucky and stupid, or never if you're just stupid'?
That claim is undoubtedly true in terms of the sheer amount of space represented by the game universe, but in real, playable terms (and sidestepping the whole 'empty space' argument), I wonder if in other MMOs, using the quickest available in-game means of transportation would reveal that it takes longer to cross those game worlds.
I suppose EVE's T2 interceptors might be the equivalent of the quickest mount in a fantasy MMO, a flying vehicle in something like Planetside 2 or a fast car in DayZ.
Anyone care to crunch the numbers for other gameworlds?
Unplanned Bonus Round
Fake Edit: Just as I was about to publish this post, I stumbled across this great forum post from 2010 at MMORPG.com, in which MMO.Maverick uses similar methodology (although he uses standard rather than fastest travel speeds) to measure the relative sizes of various MMO universes.
Here is a summary of his findings:
World of Warcraft: From Kalimdor North to South Coast = 42 minutes. Lord of the Rings Online: From Celondim to Rivendell = 45 minutes. Guild Wars 2: Tyria East to West = 46 minutes. Rift: Crossing world map East to West = 30.5 minutes.
As a final thought (I mean it this time), Guild Wars 2's world of Tyria, as shown in the map below, is apparently 13 miles (21 kilometres) from east to west, which is only a fraction longer than a single Titan (the 18km Leviathan and Ragnarok) in EVE.