I can tell you now there are countries where it isn't optional. It probably depends on when you're there and where in the country you are, as well as what you look like. I was driving through Russia in a right-hand-drive vehicle which has roughly the same effect as writing CHUMP in foot-high letters on the side of your vehicle. We got pulled over 12 times in one day by policemen looking for bribes, when we had done nothing wrong (if you do actually commit a minor traffic offense and get pulled over, they're even more aggressive about getting money out of you).

It is perfectly possible to get through without bribing them in cash, and we did - we only ever gave out cigarettes. At one point though they did take one person from our group away from us, to a windowless cell with a chair in the middle, and interrogated him for a while. They were just trying to scare him into giving them money though, we managed to get out of that through a combination of persistence (both in not relenting, and pretending we didn't understand their broken English), name dropping ("I want to speak to the British embassy") and one of our group bursting into tears (no one likes dealing with someone crying, including Russian policemen).

I haven't been to Ukraine, but people I spoke to who took that route found it to be even worse than what we experienced in Russia.

Oh, and fun fact: The Western-most country where a policeman wanted a bribe was the Czech Republic. I was surprised!