Kris over on the WoW LJ has an interesting question: what's the most popular server in the game? Blizzard never has (and likely never will) singled out one server as the most popular in the game, as the QQ that would ensue might bring the forums down (not to mention that it must change pretty often, as people transfer and reroll on other realms. It seems that everyone on a high population server thinks they must be top dog when they see queues during prime time, but the most widespread concrete numbers we have are probably from the unofficial Warcraft Realms census: they claim that, with over 35,000 characters on it, Whisperwind is number one.
Of course, even that can't be trusted -- those numbers are picked up from the site's addon, all within the last 30 days, and it could just be that WR has more info about more people on that server. But at the same time, I'd guess that Warcraft Realms' numbers are in the ballpark, as long as you're talking about Yankee Stadium. Whisperwind, Cenarion Circle, Stormrage, Moon Guard, and Proudmoore are all big servers, I can promise you anecdotally, while Laughing Skull, Blood Furnace, and Malorne are definitely at the other end of the spectrum. As for a most popular realm, there probably isn't one specifically (it changes periodically, if not even at different times of the day). But if your realm is near the top of Warcraft Realms' list, it's probably busier than the others.