Let me start by saying that I am a huge fan of Voigtlander lenses and this post may end up being somewhat biased. However, I am confident you will find at least a couple of appealing reasons to take a look at them.
Voigtlander was originally an Austrian company founded in 1756. They have a long history that I am not going to delve into here, but I will note that currently it is just a name owned by Cosina - a Japanese lens designer and manufacturer. That is why you will often see people calling the lenses CV (Cosina-Voigtlander).
When we consider the package as a whole - price, size, weight, features - I think Voigtlander lenses deliver consistently one of the most balanced products on the market (with the assumption that people prefer smaller lenses and do not need autofocus). Great build quality, easily on par with everything I have seen from Zeiss; competitive pricing; unique lenses, that do not have equivalents in pretty much any current system.
The sad thing is that Voigtlander stopped production of some of its DLSR lenses, which were the proof that pretty much everything we see nowadays is overpriced. The best example would be the Apo-Lanthar 125mm F2.5 macro - it now sells for more than 2000US on ebay, while its original price was roughly 600 euros/dollars while it was in production (2002-2007). Other great lenses they stopped producing are the Apo-Lanthar 180mm F4, Apo-Lanthar 90mm F3.5 and, more recently, the 58mm F1.4. The rest of the DSLR lenses will probably follow suit and drop out of production soon. Very sad and disappointing, and I would be very interested as to the reasons behind this. My uneducated guess would be that they compete too much with the Zeiss lenses, which Cosina are also manufacturing.
Right now, Voigtlander seems to be concentrating on their M-mount lenses, releasing new models and improving old ones for digital sensors. And they have some gems in that line. A rather small 15mm F4.5 lens with a 58mm filter thread; a small 21mm F1.8 one, also with a 58mm filter thread; 35mm F1.2 with a 52mm filter thread; 50mm F1.1 with a 58mm filter thread; and these are not simply interesting specifications, the performance of these lenses is outstanding and all of them cost 1000 dollars or less (compare that with Zeiss or Leica prices).
Unlike most modern offerings, Voigtlander also try to keep filter sizes consistent - which I find to be an issue with current Sony, Fuji and M43 offerings - a very important convenience feature, often neglected in reviews.
With current mirrorless offerings - and more precisely Sony's affordable Full Frame a7 series - we finally have proper access to these lenses. Up until now it was either buying an under-featured and expensive Leica, or using them on smaller sensors.