That day is May 7th, 2014.
As of that day, only people who donated to them in 1998 (!) or supposedly people running a D-Link router (what about everyone else with dyndns hard-coded!?) will continue to have 'free' services, the limitations of which will be unknown until possibly a month after that date. As for everyone else--myself included, though supposedly one of my domain names was from my old DIR-615 router--you're out of luck. No more free DNS for you. Pay up or shut up. Oh, don't worry, they're offering their paid service at 25% off..........for the first year of course, at which point you pay them normal price every year afterward until you decide you don't need their services.
Frankly, it's bullshit.
The whole reason routers have this service hard-coded into the firmware is because it was free and always available. That they turned around and are converting that market presence into change is filthy and I refuse to give them my dosh out of principle. Sure, it's cheap! It's like $20/year! That's about half a penny per day! But that's not the point. The point isn't how inexpensive it is. The point is the principle of the thing. Had it been a paid service to begin with, that wouldn't irk me so badly. That it was free for so damned long and suddenly, "Oh nope, sorry, pay up scrub!" is where I refuse to give them my money.
So, like any good leech of the web, I went looking for alternates and, fortunately, found some. You've got no-ip.org, which isn't bad except that it looks suspiciously like DynDNS.org did while they were transitioning to their paid model (making me worry they'll be next to pull this bullshit). Worried about that possibility I kept digging and found a wonderful little article from last year that has some great options. Feel free to peruse:
http://www.gnutomorrow.com/best-free-dynamic-dns-services-in-2013/
Personally, I went with the Afraid option. It's super-basic, super-free, and super-awesome. My address is so much cooler now.
Viva Freedom! 