What are the most number of consecutive double bonds carbon can have

[bananan]

as there are dienes, trienes, qua-enes, etc. allenes

and what limits it or prevents it from continuing on.

i.e
c=c
c=c=c diene
c=c=c=c triene-enes
(c=c=c=c=c=c=c=c)n

with each end "capped" by a -CN

 

[chemisttree]

Longer than I think nomenclature could easily describe. Extremely long polymers of acetylene have this structure without the cyano caps of course.

You can read more here,

http://en.wikipedia.org/wiki/Polyacetylene

 

[Chaos' lil bro Order]

There is no limit to 'ene' length. One point of interest is that alternating 'enes' and 'anes' (aka, C=C-C=C-C=C) called conjugated 'enes' are the molecular basis for producing color. The longer the conjugated molecule is, the longer the wavelength of its emitted light. Of course, the doulbe bond doesn't have to be C=C, it could be C=N or C=x, as long as the molecule is conjugated.

 

[GCT]

bananan, you may want to understand the actual geometry of an allene.

http://wps.prenhall.com/wps/media/o..._Resources/Chapter_08/Text_Images/FG08_01.JPG

How would the carbon on the right be configured in terms of pi molecular orbitals to arrange for the second bond? Would this second pi molecular be uniquely bonded to the next adjacent carbon on the right, or would it also have some interaction with the carbon on the left?