As others have mentioned, the space between stars is vast, but also it's actually very hard for stars to directly collide.

The reason for this is because the dynamical systems of gravity, conservation of momentum etc. tend to pull approaching stars into orbits around each other or make them slingshot away after a close approach, rather than collide directly. Even though intuitively you feel gravitational attraction would make it so that they pull together, the mechanics tend to prevent that from happening. It's the same reason that, unintuitively, it takes a lot of energy to bring a rocket from a stable orbit down to Earth.

That's not to say that direct collisions won't happen, the circumstances will surely be there for them to happen, with all those millions of stars, just less likely than you'd think.

When two stars collide it's usually because two stars are in close orbit and something causes an orbital decay, such as one leaching matter from another, or another star passing close enough to disrupt it. This last point is probably more of a catastrophic risk here; even more so the possibility of a passing star slingshotting planets away into open space.

Source: this was part of my undergrad thesis.