Vodafone offers excellent coverage, both in the UK and overseas. Of all my friends who use various networks, it is us Vodafone users who never seem to have any problems with reception when others do (except in the tube, basements, etc). It might a bit pricey compared to other networks, but it's worth it. Vodafone also offers a wide range of flexible price plans to suit your every need. The staff in the store are also very helpful, including one young man who sat with me for 2 hours to try and help me sort a phone contract out.
Vodafone refused my application for a phone contract twice. First it was because they couldn't find my post code, which obviously existed since I had a bank statement saying so and have had multiple successful deliveries to my flat. Then because they discovered it wasn't registered with Royal Mail and that my building, a new development, registered another post code, the sales assistant sent them a second request for a credit check (and I have a healthy bank balance) explaining the situation - and they refused it again. Vodafone promised they'd get back to me, took scans of my photo ID and bank statement, and to this day I never got a reply nor an explanation about it.
Whilst the service they provide is good, their customer service and follow-up is left to be desired.