First of all, the only paradoxes that involve negation and self-reference are logical-mathematical paradoxes, such as Russell’s Paradox and the Liar Paradox.
Second, not all logical-mathematical paradoxes, not all of them involve negation/self-reference, for example:
The Raven Paradox
The Sorites Paradox
The Coin Paradox
The Riddle of Induction
The New Riddle of Induction
Third and most importantly, logical-mathematical paradoxes are not the only paradoxes, and they are not always the most interesting ones. The really interesting ones often concern psychology and economics and the like, for example:
Orlov’s Paradox—the more computers make work unnecessary, the more work we end up doing.
The Slacker’s Paradox—the more people try to avoid work, the more work they end up doing.
Stockdale’s Paradox: Self-belief leads to success but optimism leads to failure.
These (and many others) are solved in a recent work of mine: