I have recently discovered that nowadays it's very easy to get IPv6 access if you're using Debian (or Ubuntu):
apt-get install tspc
ping6 www.kame.net, it should work out of the box. A 6to4 tunnel should have been automatically established to Hexago, which hosts www.freenet6.net. You don't even have to register for an account, although it might be a good idea to get one if you are really planning to use IPv6, as the anonymous tunnel broker is rather slow (I had ping times on the order of 300-500ms), and you will probably want a statically allocated address space. Moreover, a tunneling protocol based on UDP which supports NAT punching is now available, so you do not need a public IP address to connect. This situation is orders of magnitude better than the one when I tried to set up IPv6 on my router at home a couple years ago.
At the moment there is not much you can do with your new shiny IPv6 connection IPv6 is still "basking" in obscurity, there's not much to see on the IPv6 web yet: dancing kame, some stats about fellow IPv6 users... Nothing really practical. However, given the trivial setup procedure, I'm sure some uses could be found. One that comes to mind immediately is SSH access. Since the tunnel can punch NAT's, even machines behind routers can be reached without any trouble. While 300ms lag is not pleasant, there is also some security through obscurity to be gained - who would bother scanning 128bit IP addresses? Of course, if you completely disable SSH on IPv4, a tunnel failure could be very unpleasant. There is still some sense having both running. For example, you can restrict SSH access to several static IPv4 addresses that you usually use; you can connect from external sites using IPv6. Besides, it's quite nice to have the ability to fix those nasty firewall setup slips when you lock yourself out by accident (that has happened to me several times).
While IPv4 is not giving way to IPv6 yet, a fair amount of software and hardware already supports the new standard. A concise overview of the advantages can be found at NetBSD IPv6 FAQ.