Reflexive tearing can initially feel wet and soothing, but if it is chronic, it will cause inflammation.
Eye drops may feel wet when initially applied, which is normal. A feeling of wetness is desirable. But too much wetness disrupts the normal layers of the tear film.
Before tears overflow (epiphora) there can be a feeling of wetness, as if you are about to cry.
When tear ducts are plugged with punctal plugs or punctal cautery, moisture is retained in the eye and there can be a feeling of wetness. In most cases the wetness is desirable and comfortable, unless the tear film is of poor quality.