These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Game Breaker: The Gifted trait. It gives you an extra point in each of your primary statistics in exchange for slower skill progress. The fact that there is normally no way to increase your primary statistics after character creation but you can still max out all important skills with relative ease means this trait gives you a huge advantage for almost no tradeoff, especially if your Intelligence is high.
With a Gambling skill over 50%, you can go to the casino in the Hub, go to the dealer by the roulette tables, hold down the 1 and 4 keys to continuously bet 50 caps, and win over 60,000 caps within 10 minutes. With this infinite source of money, besides being able to buy tons of stimpaks and some really great weapons and armor, you can buy skill books from the library in the same area of town until you can't gain skill increases from them anymore, ending up with around a 90% level for each skill.
Jerkass Has a Point: The Overseer banishing you despite all you had done was a horrible thing to do, but Fallout 2 shows that his predictions about the consequences of your actions for the vault proved essentially correct.
Tearjerker: For every animal lover, the first time Dogmeat dies. And the second time. And the fiftieth time...