Is it alright to leave a PS2 on all night?

Applies the same principle with all machines, they get hot and this can in the long run harm your system and reduce the its life span. It's better just to turn it off or at least in a suspend state to allow preserve the system.

About five years ago I was playing Spyro on PS1 and I accidentally forgot to turn it off before leaving for more than two weeks on a trip. When I got back, I found it still working, and I even finished some more levels without any problems.

I don't even turn off my PC at all now, since I'm using it all the time.

All modern tech, assuming you're not leaving it under blazing summer sun or in some other obviously horrible conditions, is going to be fine. Just be aware that it'll keep adding to your electricity bill.

The answer varies between system to system, and the setup of that console. The age of the console is probably another factor you'll want to account for, as components like the fan will probably become damaged/weaker over time.

For example, I own a: Wii, xBox 360 and a xBox One. Sometimes, I would neglect to turn the Wii off, but it was okay, as it was well ventilated. I used to keep my 360 on all night, to allow to download large games; I can't do that anymore, as it's now in a cramped space. With my One, it has a low power feature, so I leave it in that when ever I'm out the house, as any updates are automagically installed, and it's well ventilated.