Yes and no. Since zone level-scaling was added to the game, you can pretty much choose to level up in whichever zone you want, and the content will scale to your level (up to a certain point). You can therefore choose to stay in the original WoW zones as long as you want, and then move onto BC, WOTLK, and so on.
It is possible that you may eventually out-level certain zones, dungeons or other content, but you could technically choose to stay in those old expansion areas, even if you're no longer getting much experience, before moving onto the next expansion.
The "no" part I mentioned pertains to certain old-expansion content that gets modified over time. For example, much of Azeroth (including the leveling experience) was physically changed as part of Cataclysm, so the original WoW zones and some dungeons are now completely different than what they used to be. If you want a true "original WoW" experience, you would have to play World of Warcraft Classic.
If you use an experience eliminator you can just stay at that area until you complete it or the expansion. Or out level it and still stay there
Expansion missions are optional. So you can. Unless you are playing a deathknight or a demon hunter
I think some upcoming patches will allow you to choose where in WOW history you want to place your characters. Maybe even move them further in time once you've wrapped of BC and WOTC?