I reckon two on the go at once is ok, so:

ping....pang....peng....pong....dum da-DAAAA, da da-da-da DEEEE, di-DOOOO....

Raak News at 10! Next!
Genre: TV.Classification: Easy.
Runkerty-tunk, runkety-tunk, runkety-tunk, runky-riddly,
Runkerty-tunk, runkety-tunk, runkety-tunk, runky-rid..,
Oooooeeeeeeoooooooooooh! Eeeeeeeoooooooooooh!
Eeeeeeeooooeeeeeooheeeeeeeeeeeeoooooooh
Runkerty-tunk, runkety-tunk, runkety-tunk, runkety-tunk, runkety-tunk etc...

[BtD] Dr Who?

[Btd] Right in one. Too easy, that one.

[Btd] No.

Raak] 'Yes Minister'?

This one turns out harder to write than you think. TV. Current.

Bi-ba-bi-da-ba-chong. Thwap!
Di-di-do-do di-di-do-do da-ya-di-da chwang
Di-di-ya-da di-di-ya-da di-di ya-daaa da-da
Daaa-daa da-da-da daaa-daaa-dayada
Dada dada da-da daaaaa (Chwoing) ....

can I join in? (Raak) Mastermind?

Lib's was Blind Date. Chalky got it ages ago.

Have we given up numbering, then?

[rab] 24?
[Kim] did we ever start numbering?

[all] I think we all got carried away and forgot about the numbers. [Btd] No. [ScipiO] No. (clue) It's an old TV series, that has often been rerun. The part I quoted is just the intro to the main theme, but I can't quite remember how the transition goes.

Currently outstanding are 12: Kim, 14: Raak, 16: rab.

That one rab just did (16?) - I think it's "Have I Got News For You"

[Darren] Congratulations, Sir.

ScipiO] I think Raak meant "Yes, you can join in, but no it is not Mastermind". Welcome!

OK, I'll do one - number 17.
Dum dum dummmmmmm, bree-di-di deeee,
di-di deeee, dee di-di-di deee,
baaa baa babababaaa, tata tata tata teeee....
deee di-deee di-dee, deee di-deee di-dee,
dee di-dee di-deee...
etc.

Well, I've got a tune in my mind which would fit your number 17, Darren, but it won't give me its title! I'll get back to you (no doubt it'll come to me in the middle of my night). :-(

[Btd,ScipiO] Oops. Btd has correctly explained my meaning.

[Kim] <wild guess>Henry's Cat?</wild>

[Brendan] No, but good guess. Right format and genre, but better known. By the way, Bob the Dog did not quite replicate my posting accurately. In the first and third lines, the "paaah" in the middle of the line should be emphasised. This is important, as it is a syncopated rhythm. The "Waaaah-waaaah" at the end should also provide a clue. I reproduce the tune here:
12.
Pa-pa-pa paah, paaah pa-pa-paaah
pa pah-pah-pah-pah pah-pah-pah-pah pah-pada-paah
Pa-pa-pa paaah, paaah pa-pa-paaah
pa-pa-pa-pada-pa-pa-pa pah-pada paah
Pa-pa-pa paaah, pa-pa-pa paaah da da Waaaaah-waaaah

[Darren] Your number seventeen. It still won't gel. Any clues?

[Darren] Bits of it feel like The Prisoner to me, but other bits ... don't.

[Darren] Bergerac? Or have we had that?

[Kim] Bananaman almost fits, but there doesn't seem to be much of a Waaaah-waaah at the end...

[rab] No. Take the waaaaah-waaaaah nice and slow.

[penelope] You're right, it's Bergerac.

[Kim] Slow waaaah-waaah leads me to Blake's 7, but I can't quite make the rest fit!

I think we need some clues. Another bit of mine goes:
Daa daaaa, da da-da-da daaaaaa, da daa daaaa, da da-da-da daaaaaaa,
da daaaa, da da-da-da daa daaaa, da daa daaaa, da DA-DA-DA DAAAAAAA.

[Raak] I think it's Star Trek (original series).

[Darren] That's it!

*Clue* The answer to mine was put forward by someone else as a suggestion to ZK's No.9, also a cartoon, which turned out to be "Dangermouse".

The only cartoon guess I can see is The Tom and Jerry Show, but listening to the theme I'm doubtful.

[Kim, rab] Ooooh - y'know ... I think rab has picked up the right clue. Weren't there TWO different Tom & Jerry productions? Each with its own tune? Is this the Fred Quimby one?

[rab] I can only surmise that you're either not listening to the tune properly (doubtful) or listening to the "other" tune, because, as Chalks says, this is the tune to the Tom & Jerry cartoons from the unsurpassed Fred Quimby. Joint honours to rab and Chalky! Sing it now with me: "Pa-pa-pa paaah, paaah pah-pa paaah...."

[Kim] Nice rendition actually! Comparing it against http://www.tomandjerryonline.com/sounds/Tom_and_Jerry_theme.mp3 it's very clearly the one.