I clean-installed Ubuntu 12.10 last weekend. Out of the box it has an Amazon icon in the side 'dock', I removed it and don't remember what it does. Searching with the 'dash' search box does bring up results from Amazon. The alt-f2 run box, while looking the same as the search box except for saying "run a command" instead of "search", does not perform the Amazon searches. Personally I wouldn't really consider it obtrusive, especially since I've been living with alt-f2 and dock autohiding. I had to go out of my way to find out how to bring up the ads.
Aside from that, I'm pretty disappointed with the desktop environment. It's pretty but managing windows is a pain (can't easily alt-tab into a specific terminal window, for instance; it also hijacks Alt key to enable menu item search). I'm looking to replace it soon, but then again I'm probably not the user Ubuntu is primarily targeting these days.
To be honest, I found the ads to be quite annoying, I usually start applications by pressing the Super key and then typing the name. I don't see how showing Amazon search results for "terminal" or "chrome" are relevant.
I am happy that they accept donations on the download page now. Hopefully this will reduce the need for such experiments.
Aside from that, I'm pretty disappointed with the desktop environment. It's pretty but managing windows is a pain (can't easily alt-tab into a specific terminal window, for instance; it also hijacks Alt key to enable menu item search). I'm looking to replace it soon, but then again I'm probably not the user Ubuntu is primarily targeting these days.