I see on job sites that many contract positions advertise a certain hourly or daily rate.
Do those rates normally include the VAT?
If this is country specific, I primarily interested in the UK.
You have to ask a specific client about this. Some do include all fees, some not. There is no rule.
The only truth is that if you don't ask, they will pay you offered price and handle the fees yourself. The only way to prevent this is to ask them.
Contract positions, almost without exception, are advertised exclusive of VAT. I say 'almost' but in several years of freelance working I've never been presented with a rate that was inclusive of VAT.
The reason for this is that everybody in the chain of employment - the client, the agent (if there is one) and the contractor are all VAT registered. Each company is claiming back from HMRC the VAT they pay to their suppliers. So when publishing and discussing rates, figures can be assumed to be net (VAT exclusive) unless otherwise stated.
That said, it is possible that an agency might deliberately fail to tell you that the figure you are discussing is gross (VAT inclusive) while you think it is net (VAT exclusive). To avoid this potential issue (again, this hasn't happened to me) I make it clear in all written correspondence that my rates are exclusive of VAT. There's no harm in spelling it out. It'll also be specified in your contract. When I deal with a new agency I ask for a 'specimen contract' so that I can review their business terms, and this is one of the points I check (of course once I have an offer on the table I'll get the contract checked for IR35 compliance).
Rates are usually quoted excluding VAT, because your VAT registered status will determine whether you should charge it or not.
More info on the VAT threshold here:
http://www.hmrc.gov.uk/vat/forms-rates/rates/rates-thresholds.htm#2