Yes you get a lot of 'this site is blocked due to being against the political, moral and religious beliefs of the UAE' or something to that end.
You wouldn't be able to download Skype, however if it is already installed it works fine. MSN messenger works fine in the UAE. It was a fun game seeing how much porn you could get past the filters
Regarding internet prices, they were very expensive at the hotel I was staying at but relatively cheap at the local internet cafe. Because the Dirham is tied to the US dollar, it is very weak at the moment, so as a tourist visiting it is relatively cheap to live in the UAE, but not if you are working there. That said wages at Etihad for full pilots are very good, plus accommodation is provided etc.
http://www.etisalat.co.ae for internet details