It's definitely possible to hitch a taxi. In most of Europe taxi drivers recognize hitchhikers and in rare cases also pick them up. Just make sure they are taking you for free before you get in. Albania is an exception, almost every driver tries to convince you he's taxi driver and that you should pay.
Common mode of public transportation in many countries both within and between the cities. It can be the cheapest alternative to hitchhiking. More information at wikipedia