There's no automatic yes or no question. It's a bit of a copout, but here's what I know. If a system is already pretty stable, it shouldn't be a problem. If it has problems, well - it's not such a good idea.
Leaving a PC on for that long just magnifies whatever problems it might already have.
I have a couple of computers that haven't been turned off (except when I moved from MD to NC) in nearly 3 years. They're fine. (I do have them on back-up power supplies covering power outages.)
believe it or not, no, especially with anything with a large psu. if you don't have a UPS or something with an active pfc, starting the thing up tends to be a chance to kill computers.
My computer has been on for two and a half years now, with the exception of maintenance and maybe one or two long holidays. The biggest risk is leaving your computer on while it is still connected to the outside world, a lot of new exploits can arise in two weeks.
A DSL user can disconnect from the Internet by turning off the DSL modem, by turning off the PC, or by going into the properties of My Network Places and disabling the LAN connection. There are a few more options but those three are usually the easiest.
If you choose the last option, you can re-enable the LAN connection without restarting your PC. However, it may take a minute or two for your computer to acquire the information it needs to get back onto the Internet (IP address, subnet mask, gateway, etc).
A router doesn't protect you from "the Internet." A firewall does that. Most routers include a firewall these days, but you don't need a router to have a firewall. You can get firewall software that runs on your PC. We can debate the merits of running it on a router versus running it on your PC but that's beside the point.
Firewalls limit access to your PC to those ports used by known programs. You can still get a bug piggy-backing through on a known port, but it is much harder for attackers to exploit weaknesses in your computer software when access to your operating system and programs is limited by a firewall.
having good firewall software lets you know what programs on your computer are trying to get access to the internet. I don't think router firewalls do that.
leaving a computer on isn't a harmful thing when talking about parts "burning out". Conserving electricity isn't a bad thing though.
Computers are designed to run 24/7. It is not going to harm a desktop or laptop computer to run all the time. However, if you use your laptop on AC all the time, it is important that you sometimes run it off the battery - perhaps a few times a month. Otherwise, the battery will be toast before too long. You may even want to consider removing the battery from the laptop if you primarily use it as a desktop replacement.
You should at least turn off your video monitor when you are away from the computer. Monitors are a fire hazard, and also use a lot of power.
Disconnecting from the internet is also a smart thing to do. If you don't want to turn off your ADSL modem, you can just unplug it from the phone line.
Re routers and firewalls: Many routers do something called Network Address Translation (NAT). Some of them call this a "NAT Firewall". It is NOT a firewall at all and it will NOT protect you from hackers. If anyone is depending on this, then their computer is not safe.
But IF you have an ADSL ROUTER, it has its own "hardware" firewall and I am told by the experts that nothing will get through, so u dont need a software firewall, but in my oppinion nothing is 100 % safe. I also have a software firewall as a 2nd wall.
but computer is fine to leave it on (i never turn mine off) The monitor isn't Just turn the monitor off and it will be fine