Both plays focus on love, and the consequences of love. They both also have forbidden love, and they both address the influence and oppressive nature of society. They both kind of involve magic. The difference is that there is really only the potion in Romeo and Juliet and much more magic in A Midsummer Night's Dream.
One point of comparison which definitely deserves examination is how the play within a play of Pyramus and Thisbe relates to both plays. It seems to me that in a sense Romeo and Juliet is the other side of A Midsummer Night's Dream - the tragedy that this comedy could have turned in to. Remember that at the beginning of both plays the position seems to be rather similar - starcrossed lovers who pursue a relationship that is rejected at the cost of death by parents and society. It is only through the intervention of Oberon and Puck that tragedy is averted in A Midsummer Night's Dream, and I think the showing of Pyramus and Thisbe at the end of the play acts as a chilling reminder of the story that could have been instead of the happy ending of the comedy.
They both have elements of comedy--R & J has the scenes with the nurse (A sail! A sail!) and with Mercutio and his wild and silly side. MSND is written as a comedy right off the bat so it's easier to spot.
Both plays have characters who are in love with someone who does not return it (Romeo is infatuated with Rosaline who does not love him...which leads him to Juliet).
Parental control is a theme that is strong in both plays. Romeo and Juliet are both controlled by their parents and their ancestors' feud. Juliet is ordered by her father to marry Paris in order to get out of their funk over Tybalt's death.
The whole reason the couple in MSND run off into the woods is that her father will not approve marriage to the one SHE loves; rather he favors the one she doesn't fancy.
A Midsummer Night's Dream certainly has more comedic elements; there is little humor in Romeo and Juliet. The common themes in the two Shakespeare plays include love (at first sight), misplaced love and mistaken identities.