Is there a way to extend electrical wire where the splices can be finished over?
I'm putting this up as an answer, mostly because there wasn't enough space in the comments. If I'm completely misunderstanding, please point it out, so that I and others might learn.

The big box stores in the US sell something called the Tyco Electronics Romex splice kit. (Model # CPGI-1116377-2.) They say the following:

Tyco Electronic's Non-metallic splice and tap kits provide a fast and reliable method for splicing or tapping 2 wire w/ ground and splicing 3 wire w/ground non-metallic cables up to 300 volts. They are designed and approved for use in rework within existing structures. Splice and Tap Kits also eliminate wire nuts for installation and replace the conventional method for adding a splice or tap for non-metallic cable without the need for exposed and unsightly junction boxes. NEC approved Article 334-40b. 


2 Wire Ccnnection
For Use On 12 or 14 AWG (300 Volt) 2 wire NM cable with ground
Eliminates junction boxes and wire nuts   
Fast &amp; simple to install
NEC compliant - article 334-40b, 2005 &amp; 2008 NEC
UL &amp; CSA listed



  NEC 334.40(B) Devices of Insulating Material. Switch, outlet, and tap devices of insulating material shall be permitted to be used without boxes in exposed cable wiring and for rewiring in existing buildings where the cable is concealed and fished. Openings in such devices shall form a close fit around the outer covering of the cable, and the device shall fully enclose the part of the cable from which any part of the covering has been removed. Where connections to conductors are by binding-screw terminals, there shall be available as many terminals as conductors.


I think it's generally sensible to use junction boxes, but it seems like this product would be technically permissible. 

Comments?

((edit, following comments...)) It turns out that the wording of the NEC is subtle and specific for a reason. It talks about "...concealed and fished...", which @tester101 pointed out means that the wire can't be stapled in place (ie, it has to have been fished in). This would seem reasonable, as a stapled wire couldn't be pulled back out for inspection/repair/whatever. So, I'd have to imagine that an AHJ would legitimately fail this particular application because the wires would be stapled below the junction box and any holes in the framing may not let the join pass through.