I have just bought an Apple Mini-DVI adaptor and wonder which DVI-D--HDMI cable I should get?
As I´m going through different stores there are two types:
18+1 pins and 24+1 pins. Can both be connected to the Apple Mini-DVI adaptor? If not which of them can?

there are two types: 18+1 pins and 24+1 pins. Can both be connected to the Apple Mini-DVI adaptor?

Yes.

The Apple mini-DVI to DVI adapter that I use with a Macbook has 24 holes, so it can accept either an 18 pin DVI-D single or the 24 pin DVI-D dual cable end.

DVI-I cable ends, with the extra 4 pins around the +1 blade, won't fit.

Ok good!
What is to recommend then? Would 24+1 pins allow higher resolution than the 18+1 for example?

What is to recommend then?

You're going into an HDTV, right? One with a DVI-D Male end would be perfect:

http://www.monoprice.com/products/product.asp?c_id=102&cp_id=10231&cs_id=1023102&p_id=2285&seq=1&format=1#largeimage

http://www.amazon.com/Cables-Unlimited-PCM-2296-06-Single-Cable/dp/B0007MWE1E

Yes, I'm planning on outputting 1080p to my Plasma Full HD TV.
Still DVI-D both comes in 18+1 nad 24+1. What is the difference?

You only need dual link DVI to drive a display that requires 2560x1600, 60Hz video--and if you have a Mac, like the Unibody Macbook w/ nVidia GeForce 9400M, which supports a res up to 2560 x 1600 on an external display. But they use mini-DisplayPort out not mini-DVI.

Essentially, dual link DVI doesn't play a role with HDTV because we're talking 1080p max with plasmas and LCDs, and because "mini-DVI" only supports up to 1920 x 1200 anyway, so it's a moot point. Just get any decent cable with a DVI-D end.

HDMI and DVI single link have the same video transmission capability and both handle the highest res of an HDTV. I haven't used this personally, it's not from Apple, but you can also buy a mini-DVI to HDMI adapter, and just use a regular HDMI cable.

Ok. The price difference of DVI-D 18pin vs 24pin is insignificant over here, I guess I´ll go for the 24 pin then.