I find that the longer you keep your system on the more problems are caused in Windows. On other forums I've been on some people had weird problems after leaving their machines on for days and days and days on end (crashes and stuff like that) and most of the time it was fixed with a reboot. So I would always recommend rebooting once in a while if you intend to leave the PC running for days on end.
I have a feeling they were using older versions of Windows such as XP though, so maybe the newer versions can 'cope' better.
As for the hardware getting damaged, so long as nothing is running extortionately hot then you should be OK. Computer hardware is generally designed to be run for long periods of time.
And your electricity bills? You'll barely notice a difference because PCs only consume as much power from the wall as they need. Assuming that whilst you are asleep and/or whilst you are aware from your PC, it will be idle, it'll be consuming a minimal amount of power and so your bills will not go up by any noticeable amount. Obviously if the CPU is always running at 100% and it's doing heavy stuff 24/7 then yeah obviously it's consuming more power and your bills will go up.
It only takes a few seconds for my PCs to boot and shut down with SSDs so there is no reason not to shut it down when I'm not using it because they're so quick to boot up again.
Usually though I have a similar system to Tremmor where I boot my desktop up in the morning, use it and leave it on for most of the day and then shut it off when I go to bed in the evening. I only tend to leave it on overnight if I am downloading something from the internet that is taking a while or if I leave it on to render a video overnight. My PC sits in my bedroom and is a bit noisy so I prefer to turn it off at night.
