Ukraine bans entry for Russian men. Can I get the cost of my ticket refunded?

Depends on your ticket. For a normal economy ticket, the airline will be unlikely to refund you anything, but you may be able to get partial or full credit for future flights. You may be able to talk them into waiving a change fee. Read the fare rules and call the airline.

This may be case for an insurance claim, provided you actually bought travel insurance for this trip. If you did: read the insurance contract and see what is covered. If you can't figure it out, call them.

Actually the ban does NOT apply to RUssians entering Ukraine by air, as confirmed to me by both IATA (who run an airline database mentioning such things) and the DPSU (Ukrainian border agency).

From IATA:

Dear Mr. Devecseri,

I would like to inform you that, regardless of what you may read in the media, our sources in Ukraine have informed us that the imposed restrictions do not affect Russians arriving by air.

Kind regards

So you're still allowed to enter, as long as you fly.