I would like to tell about my two most recent border crossing experiences, both of which involved a careful check of my duration of stay in the country and whether or not I had registered with the OVIR.
1. Borypsil Airport, August 2010
I had a new visa from the Krakow Ukrainian Consulate on the heels of a [in hindsight rather pointless] 3-month visa. After asking around online and talking to the Kiev central OVIR, I had concluded that the new visa would probably allow me to have 90 days in the country before being required to register. At the border checkpoint at the airport I was told that this was not the case and that the new visa had no bearing on the 90/180 rule. In essence, this means that under their interpretation if you stay in Ukraine 80-90 days without a visa and leave to get a visa, after reentering the country on visa you will have to register promptly before being allowed to leave the country without paying a fine, even if you only spent 0-10 days in the country with your new visa. However, the central city OVIR may have a different interpretation and may decline to register you until closer to 90 days have passed since your most recent entrance to Ukraine.
Basically, the border guard told me I was in violation and had his boss come out to talk to me. The boss say I would have to pay a fine, emphasizing that the procedure took several hours to write up properly and that I could "take a later flight." I was already almost late to my flight because of issues with my carry-on baggage, which included some metal backpacking gear, and the guard new this because he had requested my ticket along with my passport. I told them there was no "later flight" and that I would not take my trip after all, but would remain in Kiev. At this point I honestly thought my chances of leaving the country were about nil, and I didn't care anymore because of all the problems and the fact that I hadn't slept at all the previous night.
After some hemming and hawing back and forth between the guards, the boss muttered something and left. The guard gave me back my passport and told me I was "incredibly lucky." I couldn't believe it.
I have never paid a bribe in over 8 years of living in Ukraine, and I'm happy that I didn't break with that tradition. I am almost certain that the border guards were setting me up to bribe them in the back room in order to make my flight.
2. Zhuliany airport, May 2011
WizzAir now flies out of Zhuliany, not Boryspil. This is good news, because Zhuliany is actually within city boundaries. I got there by bus for 2.50 UAH (31 US cents). At the border crossing, the guard entered my information into the computer and looked carefully at my visas, stamps, and registration. The registration covered my current stay in Ukraine beyond my exit date, so there was no problem there. But he noticed that there was a problem before the registration -- the same "problem" that the previous border guards had noticed. He spent several minutes talking to his colleague in the booth about the situation, then went out into the back room to talk to the boss. As he was returning down the hall, I heard (in Russian) -- "if he's got that mark [i.e. OVIR registration], that means he's already paid [a fine]." I gathered that the border guard was inquiring about the possibility of fining me for a past infringement. Finally, he came back, apologized for the delay, smiled, and gave me my passport.
Moral of the story: airport border guards are looking at your residency information very carefully these days.