Various mirror sites are going up; e.g. wikileaks.ch in Switzerland and wikileaks.se in Sweden. Best bet is probably to start with the Wikileaks Twitter feed and Facebook page, since the powers that be seem to be shutting some of the mirrors down as well, or blocking the DNS lookups.
Here's one that's working at the moment: http://220.127.116.11.nyud.net/. Note that a lot of mirrors will likely feature the requirement that you use a numerical IP address to visit them.
[Added] The BBC says the DNS shutdown was due to the provider responding to massive DDoS attacks.