Do you unplug your television when it's not in use? It has an ac adapter, it's built in. Same with virtually all of your home entertainment equiment. The Wii's power adapter is external for several reasons.
1. Reduces internal heat.
2. Reduces product size.
3. Easier to make it internationally universal, due to the need to only change the shipped ac adapter, not an internal part.
Your friend ( ) probably has a father who hates the electric company. If you leave the Wii plugged in, it will consume electricity, but how much, well, not much at all.
So leave all of your stuff (with the exception of the iron) plugged in. You'll be fine. And if you still have a question about the safety of leaving things plugged in, follow Nerofog2005's advise and consult your owners manual.