You know, Elizabethan stages were generally pretty small. That means the use of props and other embellishments on stage had to be fairly limited. Instead, costuming was significant in establishing character and place. While there's no way of knowing what props were actually used over 400 years ago, we can assume several: a book or journal on which Hamlet writes his intention to seek revenge for his father's murder; some tokens which Hamlet originally gave Ophelia and which she returns to him; a book for the pacing Hamlet; clearly knives and sward and daggers; the wine cups so important in the last scene. Other than that, I don't think much would have been used. Even props used as scenery would have been minimal, I'm sure, as Shakespeare used dialogue to establish time and place much of the time.