Bought Gothic 2 this week, but absolutely cannot install the game. I've downloaded it 4 time,s both using the downloader and the browser. I've downloaded it to different drives on my system.
I keep getting a notice that the files are corrupt and the installation fails. Any suggestions? Feeling kind of ripped off at the moment.

Maybe try disabling any Firewalls or Antivirus you have running before downloading.

Do you have anywhere else you could try downloading the game (friend, school, relative etc.)? You could also try another browser as well. If you opt to disable firewall/antivirus you better make full system scan afterwards as thats like inviting viruses/malware to your computer.
Do you by change have wireless internet connection? There have been couple people in US having similar problems. Servers hare in Europe but that should not matter unless there's some faulty hardware along the way from servers to you. Maybe some day if GOG proves succesfull, they'll be able to buy/rent a file server in US as well.

Well, I guess I'll trying plugging into my wireless router today, but if that doesn't work, I'm out of ideas.

I was talking more about modile broadband and the like, not inhouse wlan network as that still uses ADSL, Cable or similar wired solution to get the data. Not much can interfere with inhouse wlan signal if the wlan router is just dozen or less meters away. In case of mobile broadband anything between your computer and signal broadcast tower can interfere with the data transfer even if you don't move your computer around. This rarely interferes with normal use but if there's lot of signal fluctuation or interferece while downloading large files there may be too much data lose or corruption for program you're using for downloading to handle. Download managers help in these cases as they do more data verification and can continue if signal is ever lost.
You should also contact GOG technical support. They may be able to suggest or provide alternate solutions.