If you don't want any collections at all, you could probably do Classic Warcraft + Burning Crusades. With each new expansion, they quickly reduce the amount of experience required (usually by 30%) per level of the older content.

Basically, you only need 70% of the experience now, that players needed when BC was current content. If you have a main team with heirloom items, this can add a further 20% additional experience to your later teams, making Classic + Burning Crusade content that much faster to blast through.

If you are questing, and decide to entirely skip collections, you'll occasionally miss out on the follow up quest, which might be a kill quest. There were a lot of collections in BC, but most of them did not lead to anything special, and skipping them did not adversely affect your team much.

Not so in Northrend (WotLK)... There are a ton of collections, which lead to kill quests, which lead to more collections etc. If you're not willing to do collections, then questing is not a good option for you to level with.

Aside from questing, you can run instances. If your team includes a tank (in particular) or a healer (to a lesser degree), the random dungeon finder will rock for leveling. It might be rough in places, example - kill trash but not able to down a boss, so do the trash and then reset the dungeon and repeat... But this is one non-collection option to use.

The other choice is PvP. Depending on your battlegroup, there might or might not be a ton of lower (non-maximum) level BG's at a given time. In general AV is the fastest BG to queue for and is the best experience from running it. Even if BG queue's suck on your server, you can queue for these all the time and run them as supplemental experience whenever possible.

Also there will be some dailies (usually collections & kills open these) which you can run once a day, for extra experience to help out with not doing collections.