Until all the light has dispersed, the laser will indeed carry on going straight.
The amount of time it takes for the light to disperse will depend on what it is going through. If there are lots of particles (like in dust, or fog) then the light waves will get bounced off in all directions, and the beam of light will disperse a lot faster. But a laser in the vacuum of space will be able to go further because there is less to scatter it.
Lasers have a special property which is called coherence, which basically means that all the light “prefers” to travel together as much as is possible. A the light from a bulb or LED has very little coherence, so the light “prefers” to spread out as much as possible. That is basically why the light from a laser travels together in the direction that it is pointed.
In the atmosphere, some light does hit the molecules of gas, any dust (which is the same dust that makes cars dirty), drops of water (like fog or clouds), and in fact anything. When it does that, it looses coherence and that bit can go in all directions. Which is why when we see the light in a laser beam, we actually see what the laser beam has lost. In a completely empty place, like deep space, you couldn’t see a laser beam.
Then there is also dispersion, like Adam says. Even in deep space, the laser beam will spread out and eventually be lost. But that could take hundreds of years, by which time the original laser device will probably be long gone!
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