Gaze means "stare with surprise, curiosity, joy, sympathy or interest"

Glare means looking at it with threatening, fierce or angry eyes because of "admiration, fear, surprise or stupidity"

Peek means "peeking" and "peeking from a hole"

Seeing means that you can only "see" by consciously using visual organs.

Watching means "watching" or "monitoring". Generally, an object should be in motion.