Can lasers damage your eyes?
Light can damage your eyes. The better question might be: How bright does a light source need to be to cause damage to your eyes?
Small red laser pointers should be very low power and not be of concern. However there is some question about how well the power ratings match the actual output. These should output no more than 5 milliwatts.
No matter what the power rating, it would be wise to never point a laser into your eyes.
Lasers are a particular hazard because the photons are the same frequency and coherent. This allows it to form bright interference patterns in your eye. You can see some of this effect when you observe the speckle pattern of a laser reflected from a wall. The bright and dark spots indicate that the light is, like waves on a pond, able to combine into areas with high waves and low waves. The reflected light isn't very bright. But a laser pointed directly into your eye could be very bright.
Very bright handheld lasers are available from many sources. These should be treated with great caution.