Here a list of such sites sorted by provider.
(these numbers are the ones which comes after +38)

Kyivstar

http://www.kyivstar.ua/en/sms
Free
work only with numbers that start with: 067, 098, 097, 096, 039, 063, 093, 068
max 100 sms/day

MTS (ex. UMC, Jeans)

http://www.mts.com.ua/eng/sendsms.php
Free
work only with numbers that start with: 050, 066, 095, 099

Beeline

http://beesms.beeline.ua
Require registration.
work only with numbers that start with: 068, 039, 063, 093, 067, 096, 097, 098

Life:)

http://www.life.com.ua/index.php?area=lifebox&lng=en&page=15-27
NEW! free.
You can send a max of 3 SMS and MMS / day.
Works with: 063 and 093.

Promotion not more available. When we will get some new info, we will update the page.

“Free World“

With it you will be able to make free calls, through a java application, to any Life:) subscriber for a max of 500 minutes in a period of 30 days.

The activation cost is 25 uah.

For to use this promotion you need:
1 an internet access.
2 a Life:) sim card or a virtual phone number.
3 a recharge of at least 25 uah.

For to activate this promotion (and a virtual number if you don’t have a life:) sim card)
visit this site:
http://www.life.com.ua/index.php?area=mylife&lng=en&page=3-500

For to call abroad from Ukraine at only 1,20 uah/min, give a look to this post:
http://en.ukrlandia.com.ua/cheap-calls-from-ukraine

Luckily there is an Ukrainian mobile provider, Life:), which offer a very interesting promotion:

“One World”

With it you can call abroad paying just 1,99 Hryvnia (0,99 uah to Russia) for every minute of conversation!

Attention!

Now it is not more 1,20 and 0,60 uah/min but 1,99 and 0,99 uah/min (last update: June 2010)

(1 Hryivnia is about 0,18 US Dollars)

If you don’t have a life:) prepaid sim yet go to a Life:) center and ask:
1 a life:) prepaid sim;
2 25 uah (or more) of prepaid credit.
3 the activation of “One World”.

If you already own a life:) prepaid sim, you can activate “One world” doing one of the following:
-Dial *143# and press the call button and follow the instructions.
-Send a sms with the text Svit ON to the number 143.
-Contact the call center at this number 5433.

The cost of the service is 5 uah/month.
At the end of the month it will be automatically renewed if you have enough credit on your sim.

If you wish to Deactivate the promotion do one of the following the following:
-Send a sms with the text Svit Off to the number 143.

-Dial *143# and press the call button and follow the instructions.

How to dial the number

UPDATE! Once you have activated “One World” you can call abroad doing the following procedure:
Seems to be not more required to dial 811 before the number. Instead you can simply dial the international prefix followed by the number.

ex. for to call London:
no more 8114420xxxxx but +4420xxxxx
where 44 is the country code of the UK, 20 is the local code of London and xxxx is the number of your home or whatever.

Further information:

Life:) One world:

http://www.life.com.ua/index.php?area=mylife&lng=en&page=3-57

Almost free calls from abroad to Ukraine:
http://en.ukrlandia.com.ua/free-calls-to-ukraine