Agree with Simon - May and September are fab months - Turkey is especially lovely at those times.
Depends on where you want to go - if you dont mind the cold/wet/rain/snow, then plan accordingly. I personally woulnt want to be in London on a wet Tuesday in January for example, but I also wouldnt want to be there during the summer as the tubes get hot, people faint, the tourist numbers are huge, everyone is cross because of the weather etc etc.
I would travel from March through to October and avoiding July and August. about 7 years ago