When zero-sum conditions appear in combat systems, it's usually due to a choice nullifying another choice - which means there honestly wasn't a choice. For example, if in a game system the only effective defense is to parry, but you have to sacrifice your next action to do it, that's a zero-sum result. It happens with weapons and armor too, where armor and weapons consistently null out one another's offensive or defensive capability. It isn't bad - there's strong real life precedent for it - unless there's nothing else in the rules to help break the cycle. This may also happen in games that force accuracy to be sacrificed in the name of damage. More accurate weapons don't do enough to get through armor while heavier weapons aren't accurate enough to hit anything.
Sometimes the mechanics tip things in one character's favor too much, and if they don't provide a way to recover it becomes zero-sum. Death spirals (as much as I like Silhouette's damage rules) are an example of this. Once a character has taken damage they are more likely to take more damage, and it just continues to get worse. This means, in most cases, the character with the first significant success will win. It also doesn't help that characters in Silhouette with identical offensive and defensive skill levels have a high probability of not being able to hurt one another - making it two zero-sum games for the price of one (you can't hit the other guy most of the time, but if you actually do hurt him now you're more likely to keep doing it).
Any point buy-type system where the net result is no change are zero-sum. This is typically intentional - for example, there's no way to be ambidextrous without either spending points or taking a disadvantage. I don't find point buys like that to be a helpful way of maintaining character balance (a concept I'm dubious of as it is). I understand the reasoning, and that some people prefer it). I'd rather have distinct spheres of character ability (such as traditional attribute/skill splits, or skill/stunt/aspect in Fate) where points can't be traded between them. Balancing that out is a lot easier than trying to figure out if +1 DEX should be worth the same number of points as being agoraphobic.
|That never gets old|
Finally, we get to my last example of a zero-sum condition in an rpg: the players versus the GM. In games where the GM takes on an adversarial relationship with the players - especially more traditional games where there's nothing the players can do about it within the system - there's typically only one true outcome. The players "lose" (their characters are killed) and the GM "wins". This is nicely summed up on the TV Tropes entry for Killer Game Master. But it doesn't have to be the over-cliched extreme of the Killer GM. For some GMs, it's "common sense" to do things like increase the difficulty of every encounter, skill check, die roll, etc. as the characters advance, in order to give players a "challenge". While it's great to tailor something to the power level of a group, doing so by rote can result in a zero-sum if everything included in the encounter completely nullifies every advantage the PCs have, then there's no real reason for the "challenge."
After all of this, it might seem logical to ask, "So what do I do about zero-sum games I don't want?" The answer isn't clear cut because it depends on the situation. Games like Fate Core address this by allowing invokes after the dice are rolled (meaning the use of the Fate points aren't a complete gamble), as well as in the concept of "failure as success at a cost". Other solutions might mean tweaking portions of the system to allow a loss for one player that doesn't automatically translate into an equivalent gain for another.
In the end, not all zero-sums are bad. Examining them is probably a good idea, though - if only to make sure that the zero-sum condition is something that was intended (or even fun).