Suggestion:
Officially? NO, there's two issues here…
1) Regional Locks — Most games made for the US systems will look for a Wii Menu version that ends with "U" (U = US / North America). UK Wii Menu version ends with "E" (E =Europe). The regional locks also apply with the different game rating systems (ESRB in the US, PEGI in Europe).
2) NTSC vs PAL — The Wii still runs on the old analog standards. US games work on the NTSC standard while UK games work on the PAL standard. Trying to run stuff across different broadcast standards will give you messed up video (or at the very least, it'll be black & white).
UNOFFICIALLY? You can, but you need to do some major software modifications to temporarily change the region of your UK Wii (WARNING: VOIDS WARRANTY) to support the US games… which becomes a major headache as you have to keep track of things that most modders don't bother with.

{ 2 comments… read them below or add one }
No. The Wii is region locked meaning that different countrys wiis play different types of games. The American Wii uses NTSC signals were as the UK Wii uses PAL signals so no. Sorry.
No you can't, but I think there is a software just like an action reply called "Free Loader", which lets you play foreign Wii disc's on the Wii.
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