Yes, in Hamlet's own estimation of himself he is a coward. It's not that he is a coward in the strictest sense of the word, however. It is not that he lacks courage and is "lily livered." No, he sees himself as a coward in that what he has to do takes him so long for he thinks too much and too deeply on it; he thinks and plans rather than acts. Maybe that's what all cowards do, but Hamlet thinks to a fault, and he knows it.
In three soliloquies, Hamlet chastises himself and calls himself a coward for pondering rather than acting:
First, in Act 2 , Scene 2, from the "O, what a rogue and peasant I am" soliloquy:
A dull and muddy-mettled rascal, peak
Like John-a-dreams, unpregnant of my cause,
And can say nothing! No, not for a king,
Upon whose property and most dear life
A damn'd defeat was made. Am I a coward?
Who calls me villain? breaks my pate across?
Plucks off my beard and blows it in my face?
Tweaks me by the nose? gives me the lie i' the throat,
As deep as to the lungs?
Next, from the "To be or not to be" soliloquy of Act 3, Scene 1:
Thus conscience does make cowards of us all,
And thus the native hue of resolution
Is sicklied o'er with the pale cast of thought,
And enterprises of great pitch and moment
With this regard their currents turn awry
And lose the name of action.
And finally, in Act 4, Scene 4, he is once more tortured by the thought that he may be a coward in the "How all occasions do inform against me" soliloquy:
Now, whether it be
Bestial oblivion, or some craven scruple
Of thinking too precisely on the event—
A thought which, quarter'd, hath but one part wisdom
And ever three parts coward—I do not know
Why yet I live to say 'This thing's to do,'
Sith I have cause, and will, and strength, and means
So, is Hamlet a coward? Maybe a bit. Certainly he thinks he might well be. But it's more to the point to believe that he loves his life, regrets that the need to revenge his father's murder has befallen him, and knows that he is ill prepared, temperamentally, to do the deed. For he is a man of thought and not of action... he is a schoolboy-prince who has to force himself into a situation and a frame of mind to finally risk his life to do what he knows must be done.