All networks except TriMob are 2G-only. I use Kyivstar which has a favourable expiry policy. Effectively you have to make a call every 6 months, but the published rules are much more complicated than that. TriMob expires without periodic top-ups. Because of the lack of 3G and 4G, Ukraine has an abundance of free wifi. Often the first thing that people ask for when sitting down in a restaurant is not the menu, but the wifi password! Also the 2G bandwidth is better than 2G in other countries, except around the main station in Kiev where it's very congested.
Also see the previous thread at
http://www.prepaidgsm.net/forum/showthread.php?t=7186