I honestly think that most examples of degenerate play in board games are either examples of broken games or player and experience. It takes games like Magic the Gathering that have a lot of intricate interactions with rules that can sometimes contradict each other to really create
Roleplaying Games, designed to cover a much broader variety of situations than a given board game, have a lot more rules and, consequently, a lot more potential loopholes to abuse. You know, things that are technically legal but shouldn't be.
And it's clearly been a problem for a long time. Gary Gygax created the demon lord Fraz-Urb'luu for the specific purpose of dealing with two problem players. I remember that since the name is pronounced Frazer Blue, which sounds like a sour candy.
Personally, I knew a guy who, back in first or second edition, combined tower shield with cestus (which is an ancient Greek boxing glove) to try and minimize weapon speed and maximize armor class. Yeah, I know that works for Captain America but it still doesn't make a lot of sense.
And, yes, I also know that that is barely a ripple on the kind of rule abuse that took place back in the day. It's just one that stands out in my brain because of the absurd image and the fact that it doesn't involve any magic or rules from different supplements.
And, as much as I loved and still love Dungeons and Dragons 3.0 and 3.5, third edition has some of the worst degenerate play. Personally, I think the Open Gaming License had a lot to do with it. An avalanche of third party supplements that were all 'legal' created an unbalanced environment. The classic example was Pun Pun the Kobold who was a thought experiment to create a low level kobold that had infinite stats, access to all spells and a divine rank (which actually just used official Wizards of the Coast rules, if I'm not mistaken)
Of course, that did involve stretching some rules to allow players to use an NPC-class and assume both divine and diabolic entities are just going to let it happen. Any game master who is actually awake should make sure that it never happens.
And let's face it, judicial use of Rule Zero, the GM gets the final word, is actually why most of these issues usually get taken care of. Of course, that opens up the other side of the table, the subject of either overly permissive or vicious GMs. Mind you, a lot of that can get filed under we were all 14 once.
I had originally been thinking that degenerate play is more common in old-school style games. However, while I don't actually have any proof of this, after some thought I changed my opinion. Old-school games are much better at surviving degenerate play. It is beyond easy to use loopholes to abuse narrative games but then those games are going to fall apart.
(I realize that all my examples are from D&D. That's really because I played so much of it over most of my RPG experiences)
There is also this about degenerate play in RPGs. It does not seem to leave as many hurt feelings as it does in boardgames. Often, there is a more rewarding sense that someone was really clever and the experiences end up being anecdotes that you bore people with over the years.