I've been watching 'Solo' and as it has sort of 'classical music' for its opening and end credits, it got me considering what other sitcoms have 'classical' musical for theme tunes. Using the term classical music somewhat loosely but you might get what I'm geting at.
The only other one I can think of at the moment is Ever Decreasing Squirrels.
Do you mean instrumental, perhaps even orchestral, rather than classical?
And do you mean Ever Decreasing Circles? 
KUA is sort of clasically sounding.
Fawlty Towers
Yes Minister
Yes Prime Minister
The New Statesman.
To the Manor Born?
Can only half remember it.
If by classical (as Aaron says) we loosely mean orchestral or anything that sounds old-fashioned instrumental, then you can say The Ghost & Mrs Muir, Blackadder, Puffin' Billy, Wings, Hogan's Heroes, That Girl, Rumpole and Never the Twain. Gentle Ben too perhaps, but not Happy Tree Friends.
Quote: zooo @ May 18 2011, 11:38 AM BSTTo the Manor Born? Can only half remember it.
Sounds very similar to Yes Minister.
Quote: Kenneth @ May 18 2011, 11:44 AM BSTSounds very similar to Yes Minister.
Almost identical in fact. I must play them side-by-side one day.
After Henry.
Blackadder?!
Got to be winner of most obscure thread. That's not a suggestion for a sitcom by the way.
The Happy Apple
The Fall and Rise of Reginald Perrin
Quote: Steve Sunshine @ May 18 2011, 6:31 PM BSTThe Happy Apple
(Which is more than I did when I watched it)
On the Up, although just the opening is classical (Handel). The closing theme is sung by Dennis Waterman.