A few days ago the muxtape guy broke silence on what's going on with him and the RIAA. Short answer: he gave up. Probably wisely.
As predicted, muxtape as you knew it is gone forever. There are, however, a number of contenders trying really hard to slide into everyone's consciousness as the replacement for muxtape. Favetape, for instance, is one of the most high-profile of the bunch. They've been doing a number of really cool things in the mixtape space, leaving me with little doubt that they're going to be the de-facto place people make their mixtapes.
Until THEY get into things with the RIAA, that is. Sure, their model does not involve hosting any files (which is pretty dang cool, actually), but at the end of the day they're generating referral revenue using content for which they don't have a license. They will get shut down too. Unless they work out some kind of deal with the RIAA -- which means you're probably going to have to pay to use them.
So where does that leave us? The best solution that I see right now is to install Opentape; it's simple, fast, and low-profile enough that your friends can continue to hear your mixes without the threat of some money-grubbers getting shut down. You COULD decide to go with favtape or mixtube or one of the others, but at the end of they day they're trying to make a buck off you -- which is the best way to ensure that they cease to exist. (The RIAA/BMI/ASCAP does not like it when you make money involving music. If your business even has a radio playing within earshot of your customers, you're required to pay them the appropriate license. Same goes for "on-hold" music.)
For the future? Hold on to your butts, for I've got a couple ideas in the works that may make mixtaping even easier with less risk of being shut down. If I have such ideas, you can be sure OTHER people do as well, which will make up for the fact that I'm notorious for getting all excited about a project and then completely abandoning it after very little of the work has been done.
In the meantime, though: seriously check out Opentape.