Oh man I love lots of them but 8 Out Of 10 Cats is top every time. It's really the only one I ever properly keep up with; the rest I just marathon five eps or so once in a while to catch up. QI is one that I loved loved loved but now am not as fond of- I still like it, but there were like five episodes in a row of series J that just did not cut it for me. I'm looking forward to Would I Lie To You's new series though. That one's also really good, but there's not enough of it.
I'm not a massive fan of these, but I do have fond memories of watching Never Mind the Buzzcocks back when Simon Amstell and Bill Bailey were still there. The level of consistency on that show at that time was greater than most other panel shows of its ilk. That, and it was hella funny and introduced the world to the craziness that was Amy Winehouse before we realised how screwed up she unfortunately was. It lost a lot of its steam when Amstell, and then Bailey, departed, unfortunately. But those few years where it all clicked were glorious. And most of them are on YouTube as well!