unless you are doing a run for S.E.T.I or other collabaration project where your compute power can be used when you aren't at the screen PLEASE SHUT DOWN YOUR SYSTEM.
You should shut the system down - not so much for Computer reasons but for ecological and "Green" reasons -- saving you money as well. -- I don't mean of course shut it down every five minutes or so - but certainly at night / if you go away on holiday etc etc.
(Of course if you NEED a server to be on 24 hrs a day then of course you have to leave it running - but even here remember most servers can be run with the screen / monitor either switched off or disconnected so you should do that too).
1) You save energy - so your bills are cheaper.
2) we don't need to generate so much power -- again keeps the carbon footprint down and hence contributes to the fight against "global warming"
3) your components aren't used as much so they shoould last longer.
Most backup options have settings to shut down the computer automatically after the backup is done. The same is true of long running downloads (even from torrents if you use those).
So there is no reason to keep computers running just because you are "Backing up" or downloading large files.
If you need to SEED P2P sources then you can do these during the time you are at your machine.
Old expression -- still valid today "Waste not -- Want not".
My only concern is that in some countries - particularly the UK where corporate greed is really rife and there's no decent price control for energy supply companies such as there is in the USA (Public Utilities Commission) is that as we use LESS energy and the profits go down then the fat cat directors will still want to maintain their disgusting bonuses so the price will undoubtedly rise to make up the shortfall so the poor consumer can't win.
However it's still a good idea to turn off your machine(s) when you don't need them.