A couple of the travel sites I use…
http://www.skyscanner.net/ – good for seeing flight prices across different providers without irritating advertisers getting in the way. They also have a view showing prices for a destination across a month so you can go when it’s cheapest. (Europe only)
http://www.seat61.com/ – train travel across the UK and Europe. How to get from the UK to most European destinations by train, approximate times and prices, and how to book.
http://www.traveline.org.uk/ – public transport in the UK. Good to find out a public transport website in an area you are visiting.