The Ukrainian official companies register can be found at http://irc.gov.ua/ua/Poshuk-v-YeDR.html. The interface and information is in Ukrainian only but Google’s translation option does a good enough job to help you through the site. If you use Google Chrome as your browser you can enable its automatic translation prompt by going to Options, Under the Bonnet, and ticking the Translate box. Many thanks to Ladymyr Bondar for alerting me to the site.
Many thanks to Britta Nordström for alerting me to this site. Business Ukraine (http://biznes-ukraina.ua/) has a useful collection of directories of companies, products and services in Ukraine as well as links to postal codes and transport timetables. There is also a list of Directories of the world on-line (http://biznes-ukraina.ua/extra.phtml?ttt=1&l=en) that is mostly yellow pages for countries around the world. The market reviews look interesting but the articles are subscription only.
There are Russian, Ukrainian and English language options for many of the sections but you may have to resort to Google’s translation service for some areas of the site.