So let's do some calculation. Let's assume you play 10 to 25 hours a week, every week, for a year. You buy 20-packs of AA batteries from Wal-mart for $9.76 plus some tax, which we'll just call $10 for the sake of round numbers. You run your single Wii remote down until it's dead each time before replacing the batteries. The following table tells you how much you can expect to spend per year for batteries based on your usage (per week) and the lifespan of your batteries.
So if you're only getting 15 hours of use before you change the batteries, as apparently is happening with my brother, then you could spend $35 per year just on batteries by playing as little as 10 hours per week. If you play 20 hours a week, you're up near $70. And if you have two Wii remotes, the cost will go even higher.
Apparently the manual discourages the use of rechargeables, although the page linked above says use Nickel Metal Hydride (NiMH) if you insist on doing so. I don't know how long those will last, but my experience has been that regular batteries will last longer than rechargeables will between charges.
These are not huge costs, but they are costs you won't see with a PlayStation 3 or an Xbox 360 controller. Naturally, Nintendo will no doubt offer a new rechargeable Wii remote very soon, giving you the chance to upgrade. I bet it won't be cheap either.
Update: Brother sent me this scan from his manual, just to point out the bit that says you should use alkaline batteries...to avoid BATTERY LEAKAGE. Of course, who reads the manual (besides my brother)?
I read in the Q&A over at Planet Gamecube that NiCads are okay too, so long as you treat them in a sane manner. The admonishment against NiCad batteries is more a CYA kind of warning. I've been using them in my own Wiimotes and have had no problems with them at all.
I get about 30 hours out of mine. Although I turned the volume down on the remote and I turned off the vibration. It really helps. The vibration isn't really strong anyway, I'm more concerned with not getting my ass kicked by a giant underwater snake, dragon thing in Zelda.
I believe there's a third party charging station being released in Q1. It's a Wii stand which has spots to plug in up to four Wiimotes (if they follow the plan of the pre-release images I saw).
It's not too pricey either. $30 maybe?
Funny, I get FAR more time out of modern rechargeables than I do from normal alkalines.
You can buy rechargeable AAs with 2500mAMPH ratings four for ten bucks at any grocery store these days. It's not even a contest anymore, alkalines are useless.