The scenario: I've got a blogger account (i.e. this one) which is linked to my google account, and I'd like to be able to use youtube and google search without being considered as being logged in. If I log out in e.g. the google search page I also get logged out from blogger. Gmail isn't an issue since I use thunderbird/evolution, but it would cause similar issue to blogger vs search/youtube.
The past year I've become increasingly annoyed by the behaviour of google applications -- they feel more intrusive and I keep on being asked to sign in and stay signed in. Without going into specifics, it's beginning to feel like Google is trying to turn the entire web into their version of Facebook. And I don't lie it.
Here's what you can do in Firefox:
1. Install the Cookies Manager+ add-on in firefox, and restart firefox
2. In firefox, go to Tools, Cookies Manager+
3. Click on Tools/Exceptions
4. Add google.com and youtube.com
Done. Now you can remain signed in to all other google sites, while staying signed out of Youtube and Google Search. Note that it doesn't make you anonymous, but it just takes care of some of the minor nuisances associated with always being tracked by google.