OK, I don't live in the UK which is going to skew things a lot, but we buy a lot of BBC programmes here (even though the BBC won't let me onto the sites of those we buy).
I've italicised the programmes (and people) I've watched or listened to, bolded the ones I love, and struck out those I've never heard of.
Newsnight
iPlayer
Website
Toni Arthur
Brian Cant
Spooks
Adam Adamant
Postman Pat
Blackadder
Hancock
Yes Minister
Later with Jools Holland
Pride and Prejudice
Hitchikers Guide
World service
Mr Benn
Glastonbury
Horrible Histories
Quatermass
Two Ronnies
Radio 3
Simon Mayo
Goon Show
Blakes 7
Last Night of the Proms
Last of the Summer Wine
Steptoe and Son
Clangers
The Young Ones
Edge of Darkness
Tinker Tailor Soldier Spy
Letter from America
The Mighty Boosh
QI
Panorama
Bagpuss
I Claudius
Absolutely Fabulous
Red Dwarf
Our friends in the North
Woman's Hour
Charlie and Lola
Alan Partridge
Likely Lads
Michael Palin
This Life
That's life
The good life
Captain Pugwash
News Quiz
Miranda
Who do you think you are
Kirsty Wark
Jeremy Paxman
Wogan
Tripods
The Ascent of Man
One foot in the grave
Rob (Webb) and Dave (Mitchell)
David Attenborough
Bruce Forsyth
The League of Gentlemen
Have I got news for you
Me & You
Doctor Who
Top Gear
Merlin
Ivor the Engine
Blue Peter
Five Live
That Was The Week That Was
The Goodies
Songs of Praise
The Day Today
Not the Nine O'Clock News
Mr Men
East Enders
Radio 1
Radio 2
Ripping Yarns
Bergerac
Radio Active
(everything on) BBC4
Only Fools (and Horses)
Sky at Night
Teletubbies
Life on Mars
A Bit of Fry and Laurie
Children in Need Appeal
Douglas Adams
On second thoughts, it may have been only our version of That Was The Week That Was that I've seen, but I'll leave it there since it was based on the BBC concept.
Also posted on Dreamwidth, with