The vote is underway all over Ukraine, and polls will close at 8 p.m. local time (1 p.m. Eastern time in the US). You can follow the action on various twitter feeds, the National Exit Poll, and many news sites (I am partial to Ukrainska Pravda). I will post updates throughout the day as well.
UPDATE (4:15 p.m. local time): The CEC just released turnout data for the first two reporting periods. Eastern regions (Donetsk and Luhansk) lead the way with 57% of voters casting ballots by 3 p.m. Zakarpatska Oblast has reported lowest turnout (35%), and one oblast has not yet reported in (Chernivets). Turnout in many western regions where Tymoshenko is expected to be stronger is relatively low (L'viv Oblast reports 46%, Ivano-Frankivsk 41%). Regions where Tihipko performed the best in the first round did not generally report high turnout; Dnipropetrovsk was just about at the mean (49%) and Odesa was below the mean (42%). As I have noted before, Tymoshenko's areas of strength have lower populations than Yanukovych-leaning regions. Large-scale mobilization of core supporters is especially important for her to have a chance at victory. Volyn, Ternopil, and Rivne reported turnout above the mean, but lower than turnout in Yanukovych's core regions. While projecting outcomes from turnout data is problematic for several reasons, on their face the data suggest that Yanukovych is likely in a better position than Tymoshenko at this point in the day.
UPDATE (8:15 p.m. local time): All exit polls are giving the nod to Viktor Yanukovych. While results vary, Yanukovych is predicted to have around 49%, Tymoshenko 46%, and the remainder (5% or so) against all.
UPDATE (10:30 p.m. local time): Of course, as Tymoshenko herself noted, exit poll results are within the standard margin of error rendering a definitive prediction elusive. While the CEC site has not yet posted results, Ukrainska Pravda currently has information on about 1% of the votes and will be updating regularly.
UPDATE (1:00 a.m. (February 8) local time): With 25% of the votes counted, Viktor Yanukovych leads 51% to 43%. Based on the SOCIS exit poll, Ukrainska Pravda has published a "portrait" of the electorate for each candidate. In most demographic features, the candidates' supporters are essentially equivalent. While I do not have the raw data to run a quick test, I suspect that there would be a statistically significant difference in supporters based on residence - with rural regions favoring Tymoshenko and large urban areas favoring Yanukovych.
UPDATE (2:45 a.m. (February 8) local time): With just about 50% of the vote counted, the CEC reports that Yanukovych leads 49.52% to 44.85% with 4.49% of ballots cast against all and 1.12% invalid. Eleven regions have processed fewer than 50% of their protocols: Crimea (15%), Volyn (27%), Luhansk (31%), Ivano-Frankivsk (31%), L'viv (32%), Chernivets (35%), Kirovohrad (36%), Sumska (39%), Rivne (45%), Kyiv Oblast (47%), Zaporizka (47%). While many of these regions are in Tymoshenko's area of strength, other high-population areas of Yanukovych support still have many protocols to finalize.
Below is a table of turnout, with results sorted by oblast. The three results are reports from 11 a.m., 3 p.m., and 8 p.m.. Given the stakes, and the decisive status of round 2, higher turnout is not surprising (although it surpassed round 1 by just a few percentage points where turnout was 66.76%). Areas with core supporters for both candidates seem to have been mobilized, but regions where alternate candidates performed well in round 1 have lower turnout (e.g., Yatseniuk's core area in Chernivets, Tihipko's regions of strength in Dnipropetrovsk and Odesa).
UPDATE (3:00 p.m. (February 8) local time): With 98.26% of the protocols in, the CEC is reporting that Yanukovych has received 48.56% of the vote and Yuliya Tymoshenko 45.85% of the vote, with 4.39% voting against all. The against all vote - citizens who come to the polls to record a vote against both candidates - could have changed the outcome if they voted for a single candidate. The against all vote could also have vaulted either candidate above 50%. I'll comment on the implications of Yanukovych's apparent win later.