Neal Stephenson wrote Snow Crash in 1992, but you wouldn't know it from reading the book. He was pretty far ahead of his time on a lot of things, and the book reads like something much more recent. (If you haven't read it yet, I can highly recommend it - it's not especially deep or thought-provoking, but it's a fun read nevertheless.) One of the ideas he came up with that stuck in my mind is the idea of gargoyles - people who go around covered with cameras, recording everything that happens around them, in case something interesting happens.
Even optimistically, I would estimate that a gargoyle system won't be practical for at least another five years. Even so, I think it'd be kind of neat to build one.
By far the most important limiting factor would be power. Such a system would need to be able to run for at least a day or two between charges, and there is a definite limit to the number of batteries I'm willing to carry around. I'm assuming power requirements similar to a laptop, and current laptop batteries last about three to four hours on average. Six to eight laptop batteries is kind of a lot to carry around in addition to everything else. :(
Another major limitation would be storage. Even a low-bitrate video stream would take up something on the order of a couple gigabytes per day, and that much hard drive space would start to add up pretty quickly. At current prices, this would probably cost about a dollar per day in hard drives alone, not counting replacements, or miscellaneous other costs.
There are a lot of things which such a rig would enable. (Take that, people who would just go and ask about practicality! :p) The most obvious application is time shifting/scaling - I could, for instance, go to class and record the lecture while I take a nap, and watch it later at home where I can fast-forward through the boring bits. Alternately, I could watch random stuff in slow motion, which is really quite entertaining in its own right.
Adding a head-mounted display to the mix puts us straight into cyborg territory. You could do any of the things you could do before, but as things are happening instead of after the fact. You could zoom in on things that are far away, or really arbitrarily enhance whatever you're seeing (night vision?). With specialized cameras, you could see outside of the visible spectrum - I hear a lot of neat stuff goes on in infrared, for example. With a few extra cameras, you could get a seamless 360-degree view of the world. Alternately, you could use some clever software to stitch the view into a 3d model of the world, like Microsoft did recently with Photosynth(?). From there you could have more clever software that does fun stuff like adding annotations to whatever you're seeing, or adds in virtual objects that interact with the real world.
By five years from now we'll almost certainly have ubiquitous internet connectivity, and that adds a whole new dimension to the possibilities, but I should probably stop writing now and post this.