When the expansion starts (less than two days from now !!), you'll either want to dive straight into the new content or finish up your old content. Depending how well Blizzard's account server holds out *cough*. To get yourself a head-start however you could gather up and complete some quests, even daily quests and turn these in as soon as your level cap is increased. 25 quests can be a lot of XP quite quickly. If you're racing for the first zones, (and there will be many who are) then you'll want every edge you can get. WowWiki has a decent list of available daily quests. Be sure to empty your quest log before starting, and pick up as many as you can. Try to avoid the ones which give low cash and XP as a reward. Then, park yourself in Ogri'la and await thursday's arrival. Now, the servers come up, you've upgraded your account and you can complete the quests in the following order :
The first three quests : bombing, banish more demons and the wrangling quest.
Hearth to Shattrath and you can turn in seven: Intercepting the mana cells, sunfury attack plans, multiphase survey, the daily heroic, normal daily dungeon, daily pvp and for great honor.
Go to SSO Island and turn in another seven quests here : Open for Business, Disrupt the Greengill Coast, Ata'mal Armaments, Don't Stop Now, Crush the Dawnblade, Know Your Ley Lines, The Battle Must Go On
Use BT necklace (If you have one), to go to netherwing island (otherwise use the scroll from the "know your leylines quest" and here you can turn in another nine quests : The Deadliest Trap Ever Laid, Disrupting the Twilight Portal, The Booterang, Dragons are the Least of Our Problems, Picking up the Pieces, The Not-So-Friendly Skies, A Slow Death, Netherwing Crystals and one of the gathering quests if able.
Fly to terrokar : Turn in the bombing quest.
After that you should head back to shattrath and take the portal to whichever city has the zeppelin or boat for your faction. With minimum travel you should be one of the few people on the island to reach level 71. Not good enough? Alright, then have a grab at this leveling guide to get you trough 70-80 even faster!
As you can see however, that's a grand total of 25 quests exactly. There are plenty more quests, some pay more, some less. Group quests and raid quests especially should be savored. Just don't go out of your way to turn them in and most certainly don't waste any time completing them on the actual patch day. After all, you want to start with Northrend as soon as possible.
Low xp quests : Avoid these if your quest log is full.
Fishing / cooking quest
Keeping the Enemy at Bay
Arm the wards
The Air Strikes Must Continue