Honestly, this is one topic I really don't know too much about. Google lets your Geographic target for your web site in Google Webmaster Tools. But what if you have a ccTLD, a country specific top level domain such as .fr (France), and you want to not target a specific country?
The Google help document on this topic says:
You can only use this feature for sites with a generic top-level domain, such as .com or .org. Sites with country-coded top-level domains (such as .ie) are already associated with a geographic region, in this case Ireland.
I checked one site I have in my Webmaster Tools account, the only site with a ccTLD and it didn't let me specify a different country. So I assume only certain ccTLDs or TLDs can set "unlisted" as an option to target all countries? Or am I missing something?
Google said, "If you want to ensure that your site is not associated with any country or region, select Unlisted."
It does appear that only certain ccTLDs let you change the geographic target, like a .co TLD. And you can change it to unlisted in order to not set a geographic target.
The WebmasterWorld thread has Tedster saying:
I've only heard one practical report about this and the recovery took many months for them, but they say it did happen eventually.
I am not sure if anyone else has experience here, but I'd love to know how quickly Google picks up the geographic target change, specifically for using "unlisted" as an option.
Update: Google's JohnMu did point out a solid distinction between setting unlisted or not:
There's actually a subtle difference between not activating Webmaster Tools owner-specified geotargeting and selecting "Unlisted". Not selecting to do geotargeting through Webmaster Tools results in Google doing geotargeting automatically (generally based on the server location), activating geotargeting and selecting "Unlisted" in Webmaster Tools results in Google not doing geotargeting.