I have a personal fondness for cards which force your opponent to choose their punishment. The most similar comparison to Run Amok is Bribery out of criminal. That card is pretty bad, though. Is Run Amok any better?
When you play Run Amok, the corp is essentially given two options. The first is to rez one or more pieces of ice, taxing the runner or ending the run as needed. But if they do that, then Run Amok has a target: and because the card doesn't specify a successful run, bouncing off a barrier or jacking out still allows you to trash the card that just got rezzed.
If this happens, the card is essentially the fourth Cutlery (Forked, Knifed, or Spooned), as an ice-trashing run event. It's slightly better in the fact that a) you don't need to have the right tool for the job. you can Run Amok on anything, and b) you don't have to be able to break it, meaning you can threaten ice destruction with 0 programs installed. However, the catch is that it only works on unrezzed ice, so sometimes you might end up destroying an Ice Wall or a Pop-up Window.
Losing ice is bad for the corp, though. If they stand to lose something important, the corp might just decide not to rez. In this case, it acts like a more versatile Blackmail, since it doesn't require bad publicity to trigger. Now every Anarch can share in Valencia's fun, and Val herself can double up to have six no-rez runs per game, or nine with Same Old Thing. That hurts, a lot.
So whichever choice the corp makes, something good for the runner happens. But the catch is that the decision of which option it is is given to the corp, not the runner. And so you have to assume that you're always going to get the worse of the two options.
So it's not a particularly consistent card, and it's never going to be an MVP of a deck. You can, however, pack things to make it better. Going heavy on ice destruction with Parasite, Cutlery, Immolation Script, and possibly Kraken will increase the pressure on the corp to not lose ice, giving you more free accesses with Run Amok. On the other hand, using rez-detterent tricks like Blackmail, Cyber Threat, or Running Interference will make the corp reluctant to hand off free runs, and will thin their ice out to do so.
All told, it's a very solidly designed card, fitting nicely in the Anarch faction. As a strong run event, it might see play in Ken Tenma, although the three influence makes it somewhat difficult to justify.