American Wii plugged in a European socket (110V plugged into 220V socket); what happened

And the solution: replace the MIDI cable. Problem went away; everything works fine.

You'd probably be fine with either a 60W or a 100W step-down converter - if the Wii power brick draws at most 52W, the transformer has to be able to supply at least that amount as well. This means that either 60W or 100W would be sufficient, but 50W would be pushing it.

However, I highly suggest just buying a new power brick for the country you live in. Replacement power supplies for consoles tend to be fairly cheap, and you're much more likely to end up with something that has been tested and works properly with your device.

When shopping for transformers to take my DS with me to Europe, I found that many people reported the transformers didn't work properly with their electronics. Buying a local DS power adapter worked like a charm, though. Best of all, it worked with 110V as well (just requires a plug adapter) so I was able to use it after I returned to the US.