ahhh I just did an assessment on R&G and Hamlet today, wish I'd come here before I started cramming today... ha;f an hour before the assessment! what a good studier I am lol...
The 'buzzwords' and 'buzzthemes' of R&G and Hamlet are, to my extremely small knowledge and capabilities:
FATE
DEATH
IDENTITY
and, two things you will want to look at, Language, and Historical Context. You may also wish to explore meta-theatre, particularly in R&G, and Stoppard's relation with Theatre of the Absurd.
The notion of fate is a great one- Hamlet is always discussing 'to be or not to be', questioning his role in fate and whether he can change anything. In R&G, Ros and Guil are presented as something akin to slaves of fate- they have no control over their destiny whatsoever- it is predetermined. "There must have been a point where we could have said no...we must have missed it" is evidence of this.
Death is a big Elizabethan theme- the ghost approaches Hamlet because he cannot move on until his earthy business has been concluded. Dealth, and also bloody goriness typical to Elizabethan Revenge Tragedy, is a big part- Hamlet will seek revenge via the sword. However in R&G death is represented in a comical, flippant fashion. However yet again fate has predetermined Ros and Guil's fate in the title: "R & G are Dead".
Identity is also a huge part to play in both roles. In Hamlet, the rich, eloquent language constantly seeks, in a self-reflexive way, Hamlet's own identity and place in a world that is in the process of changing from a traditional world (divine right of kingship etc) to new ideas, and new ways of thinking- Hamlet is a novus hommo, a new man, who begins to think in a Humanist way (echoing the historical context of the transition between Catholicism to Protestantism of the times- the religious and thus also social upheaval). Ros and Guil actually have no idea who they are, or even why they are in particular places or for what reason- "we were summoned, and now we are here" is all they can think of. Even their stichomatic word games- "I'll Hie you home!" "Who are you?" "you're yourself" show that language- the only tool which they can use to communicate- is meaningless.
Stoppard's focus on marginalised characters such as Ros and Guil, also his focus on the meaningless quality of language (so different for Shakespeare's prose, here is colloquial, even crude lines) is typical of the Absurdist Theatre which focuses on absurd things, such as language, and any past beliefs, typical of the 60s movement in which the movement from Modernism to Post-Modernism (I'm not sure of that actually, but it seems about right( beliefs led so many to question what was previously taken without question.