Another way would be to do this:

ode1 = {x'[t] == -1, x[0] == 1, y'[t] + y[t] x[t]^2 == 100, 
y[0] == 10, WhenEvent[x[t] == 0, "StopIntegration"]}; sol = NDSolve[ode1, {x, y}, {t, 0, 3}];

Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"];
ParametricPlot[{x[t], y[t]} /. sol, Evaluate[Flatten[{t, InterpolatingFunctionDomain[x /. sol[[1]]][[1]]}]], 
AspectRatio -> 1]

Cheers,

Marco

Well, you said

"stop at a specific point when a variable reaches a certain value"

so you probably need to know the value? Or a condition that needs to be fulfilled to stop the integration?

And yes, x[t] will continue, but that is because you get an interpolating function that will extrapolate outside the known interval.

Best wishes,

Marco

Many thanks. Your answers were really helpful, "WhenEvent" does it nicely :)