Many hitchhikers say it's dangerous to hitchhike in Ukraine. Though, if your Russian is good enough, and you feel like it: just go for it!
When hitchhiking in Ukraine do not be surprised if you are occasionally asked for money from drivers. It is not often, however, but it occurs. Of course you can always tell the drivers
The state of the roads are pretty dire in general, and the biggest problem is the distances involved are usually pretty big (for example Lviv to Kyiv is around 550 km. In winter Ukraine can get very cold, for example January 2006 it hit -35 degrees, which makes hitchhiking very dangerous. The cost of train travel is very cheap - usually around 1 euro for every 100 km (for overnight sleeping carriages), so bear it in mind when going from city to city.