Did someone say before you've far too much time on your hands?Depends entirely upon where the object is fired, what direction, what speed and even composition. If we're talking about a battle in the near vicinity of a planet or its sun, then if the ammunition has less than local solar escape velocity then it will enter an elliptic solar-centric orbit. If not, then the star (and the planets plus other stuff in the solar system) will likely bend its trajectory anyway.
Once you start dealing with planetary and larger masses the pull may not feel that great, but it's there and will have a cumulative effect. The Earth's orbital velocity is about 67,000 mph (19 miles per second) and that is pretty much the same velocity that anything locked into Earth's orbit will have. Fight anywhere near a Jupiter size object (and we've detected bigger orbiting other stars), and the escape velocities start going up drastically. It might even become both a concern and a tactic ... ISTR reading this somewhere or other.
And that's assuming the ammunition is headed out-system - start firing it in-system and the game gets nicely complicated, especially when you take account of such things as metallic objects interacting with magnetic fields or solar heating causing the surface to start boiling off or even just differential temperature changes. I've written a couple of simulations to explore this kind of thing - ages ago, though, and I no longer have the source code. Having said that, it shouldn't be too hard to write one from scratch ... added to my exponentially increasing list of things to do!