hardware dependencies on digital distribution

I have a few questions related with how different systems work in terms of digital distribution.

Let's say I have an account in XBL, PSN or Steam and I purchase and download some games to play. After a while my system breaks, there is some new generation, I move to a different house and do not share the previous system or for any other reason I get a new one (new as a piece of hardware, not necessarily the next version of a console, it may be just like the old one, but new).

The question is: Can I simply log in with my account in the new system and download again my games so that I can continue playing on the new system?

I also wonder about the saved games, which may be in a HDD, is there any option to transfer them to the new system? (assuming the old one still works as to upload them to the cloud or whatever)

Thank you very much.

Can't speak for PSN, but I know you can on XBL. You need to have the system connected to the net when you launch the title though after you've downloaded it.

With Steam you just log-in and download your title again. Some games will even have your game saves as well.

You shouldn't have a problem with PSN, Xbox Live or Steam when you need to re-download anything on new hardware so long as its on the same generation console. Each one has there own restrictions on how they handle DRM on new hardware, but it shouldn't be a problem if you have the account they where purchased under. And saves can just be saved to a memory card or uploaded to the cloud and transferred.

On PSN you can only download each game twice now. They reduced it awhile ago to stop people sharing. Glad that it sounds like Steam isn't like that.