Depends on the lib. Max safe int size is like 9 quadrillion. You can safely deserialize serial bigints to this without ever worrying about hitting that limit in many domains.
2^53, to be precise. If your application involves assigning a unique identifier to every ant on the planet Earth (approx. 10^15 ≈ 2^50), you might need to think about this. Otherwise, I wouldn't worry about it.