There is no maximum as such for how strong a gravity field can be. However, a strong enough gravity field can reach the point where spacetime is bent to the point that no particles can escape, even if they move at the speed of light. As a first approximation, you can think of it as a gravity field so strong that the escape velocity is higher than the speed of light (however, you will need to account for relativistic effects when considering this in practice).
As >>38 mentions, a black hole is the prime example of this.