Each time you upgrade Ubuntu you have to tweak your Wine repo for the newer version. This is not a huge problem, you can just follow the instructions on Wine's site which are nice and clear.
Karmic seems to be a little weird with this. The issue comes when you want to actually install wine through Synaptic. You can't install the package "wine" anymore, you get an error like this: "wine: Depends: wine1.2 but it is not going to be installed". You can fix this easily by just installing the wine1.2 package, but it is kinda weird that they did not set up the dependencies properly. Oh well.
So in short, to install wine:
1) Follow the instructions to add the Wine repository.
2) Go to System->Administration->Synaptic Package Manager
3) Search for wine1.2
4) Install the wine1.2 package by double clicking it. Accept any dependencies it asks for.
5) Click Apply.