Ken: Countdown have (or had until recently) a rule that you have to wait ten years before you can apply again after appearing. One of my mates has been on Mastermind and Brain of Britain several times, with only a year or two's gap, so it varies between shows. In case you're interested, he got to the Mastermind final and went to the US to film a piece about his specialist subject.
Surprised nobody has said Eggheads - I like The Chase best then Eggheads but I do enjoy Tipping Point. The one I can't get my head round is Pointless - I don't think I've ever got a question right in the end round! As for Richard, well he comes across as so smug but its easy when you've got the laptop in front of you! Love the Sinnerman - anyone know how he is doing?
I watch hardly any telly but I enjoy Only Connect if I remember it's on.
Round Britain Quiz on Radio 4, with it's incredibly convoluted cryptic clues, is fantastic though - even if I am often left struggling to work out what's been going on after the solution has been provided!