Is a billion volt electrical transmission line possible? Because
$$
P_{\,\displaystyle\rm loss}=\frac{P^2R}{V^2}
$$
in an electrical line where $R$ is the total resistance
Why not use a $1$ billion volt line instead of a $800\,\rm kv$ line? Is there a maximum voltage that copper can carry?
 A: Such high voltages would be hard to create, and would easily slip away into the atmosphere like thunderbolts, creating very hot plasmas around the copper lines, eventually melting the copper lines.
Apart from that, given a perfect isolator around the wire (most likely infinite vacuum), there are no special limits for copper in itself. It's just the large electromagnetic forces in other materials around the power line that makes a problem.
A maybe better way to carry around large currents is through super conductors, there are/were actually superconductors in use at CERN, which make ordinary cabling look a bit ridiculous.
A: The energy will start dissipating in the atmosphere as corona losses, also the high tension(potential difference) between the wires and the ground will make it dangerous. There maybe electrical breakdowns and electric shocks which will then fry the wires along with causing damage to nearby objects and people it will also breakdown the transmission by destroying the transmission cable.
Asides from these, the magnetic interaction between two lines carrying such high voltage current would be extremely high to be handled easily. So yes there must be a limiting potential which would be decided by calculating all the above factors.
A: Another limit on overhead power lines is temperature. High temperatures weaken the heat treated aluminum allowing it to fail with modest winds, or ice. Also it stretches the cables causing sag and making contact with trees (a bad idea). Most composite lines (ACSR type) have a limit of 93°C. Newer hi-temp designs can go up to 300°C. The best currently is the 3M ACCR conductor.
A high voltage line means big cross section on the wire and thus weight. The higher the weight the shorter the span needs to be to keep the towers from becoming super tall and expensive. Lots of small spans is also expensive. So there is a trade-off between wire section and cost.
Lots to read at http://www.scribd.com/collections/3745105/Overhead-Conductor-Manual
I think high voltage is for sure going to have problems with corona (as mentioned), but also there are losses that come from eddy currents and skin effect which only increase with voltage.
PS. The highest voltage powerline I know of is rated at $1300 \rm kV$ I think. 
A: It might not be impossible, but it could be cost prohibitive.
For a suspended wire, air will breakdown when the electric field strength is around $3*10^6 V/m$.  As the potential gets higher it becomes much more difficult to keep the fields around the transformers and supports from causing the insulators to ionize and spark.  All insulators have a breakdown point as well.  A partial breakdown is known as the coronal breakdown as others have mentioned is also a design limit.
The ultimate limiting factor is probably in the design of the amorphous metal transformers (limited space for insulation and reducing electric fields) to handle such high potentials without arcs or thermal problems due to current (on the lower voltage side).  Also insulators and supports become expensive and difficult due to the amount of physical insulation needed at 1 billion volt potential.
Simplistically a single wire carrying 1 billion Volts would spark if $E=3*10^6=\frac{(1*10^9)}{height}$ where $height=333m$.  You probably need 3x times that for margin as the line voltages can spike and breakdown field of air is variable depending on many factors.  You wouldn't be able to run multiple parallel wires in such a high voltage system which is also a huge disadvantage.
Currently the highest target (system in India) is 1200kV which would spark at a distance of 0.4m so you can see there is a lot of margin needed in the system for parallel lines.  If you assume one line is at -1200kV then they would spark at 0.8m.
