Gaze, gape, stare, glare, peer, gloat are comparable when meaning to look at long and attentively, but they vary greatly in their implications of attitude and motive.
Gaze implies fixed and prolonged attention (as in admiration, curiosity, or wonder).
Gape adds to gaze the implication of stupid and openmouthed wonder or indecision.
Stare implies a fixed and direct gazing at a person or object; it may connote curiosity, astonishment, insolence, or vacant fixedness.
Glare adds to stare the implication of fierceness or anger.
Peer suggests a looking narrowly, especially with or as if with partly closed eyes, or curiously, especially through or from behind something.
Gloat usually implies prolonged or frequent gazing upon something, especially in secret, often with profound, usually malignant or unhallowed, satisfaction. Sometimes the implication of malignant satisfaction is so emphasized that the implication of gazing is obscured or lost.