In many countries, you can not give up your right to sue. For example in Australia, when you go skating and there is a sign "Skate at your own risk" it means nothing.
A lawyer needs to chime in, but I believe those signs in the US may only help some in cases of accidents. Just putting up a sign that says 'do X at your own risk' does not suddenly free the liable party from being sued for something happening due to negligence.
In the U.S. the sign would be relevant only to the extent that it would support a finding of contributory negligence (i.e. you were aware of the risk and took it anyway), which would be the case in Australia too since it's a common law concept. It would not bar a suit.
In general, you cannot in the U.S. sign a blanket waiver giving up your right to sue. Waivers are generally narrowly construed to limit their scope to what the parties foresaw, and some types of waivers are just void as against public policy. For example if you sign a waiver of liability when you go skydiving, it might protect the skydiving company against a suit if you land the wrong way and sprain your ankle, but it won't protect them against a suit if the pilot was drunk and the plane crashes.
I know this is fine when everyone is being moral/rational. But what prevents someone from maliciously suing the skating (or something more dangerous, such as skydiving) place for something they weren't really responsible for?
Nothing. But to win they would have to show that the company really was responsible for it, since the accused is innocent until proven guilty. The accused can also request a trial by jury; 12 people generally make the right decision.
(Note: not legal advice, and possibly only relevant to the US)
