<map lat='49' lng='32' zoom='5' view='0' float='right' width='430'/> Generally, hitchhiking is quite okay in Ukraine.
The biggest problem you could meet is that the majority of the people don't speak English or other foreign language. Though, if your Ukrainian is good enough, and you feel like it: just go for it! Most of people speak Russian too. Besides, if you speak any of Slavic languages, the connection will be much easier, they are quite similar. :)
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 that your don't have money and that you are hitchhiking.
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). It is allowed to hitchhike everywhere on the roadside, you just need to find the most lucky place. In winter Ukraine can get very cold, for example January 2006 it hit -35 °C, which makes hitchhiking very dangerous. The cost of train travel is very cheap – usually around one euro for every 100 km (for overnight sleeping carriages), so bear it in mind when going from city to city.
Of course you can get stuck easily because of night on highway next to turn away from main road. But there are also nice night-traffic of trucks caused by warm weather from may to September. Usually there are some gas stations near to such places and there some favorite and famous places for stops known by drivers - something like unofficial rest-stations (There are no official but a lot of unofficial ones). You can easily find something to eat and to drink there or at almost all gas-stations there are night-shops. You can eat in some road-restaurants, they may be not expensive for foreigners from countries like UE ones - you would probably have some nice dinner there for $7-10 (2008).