Magnetic field of less than 60 Gauss (magnetic field measurement unit) will not affect your watch. Any stronger fields may disturb its performance.
On a quartz watch, the effects are temporary: the watch stops when in contact with the magnetic field, continuing again when away from the field.
Effects on an mechanical watch are more damaging: the watch could stop altogether or have timekeeping difficulties until it is repaired. Try and keep your watch at least 5cm away from magnetic devices.