I'm an only child, and my mother put me as a co-holder on all her accounts (bank, etc.) before she died. It prevented all of that stuff going through probate, and also helped because she got terminal cancer and in the last couple of months, it was very helpful to have access to her checkbook, e.g. to pay her utility bills and stuff like that.
The one thing she didn't manage to get me on was the home, so that did have to go through probate. It wasn't a huge deal, but it would definitely have been easier without that.
In terms of any liability, that depends on how much you trust your parents! :) If the home is paid off, they are responsible with money, pay their taxes on time, etc., then there's no problem for you.