One of my favorite ironic moments of the play is Romeo's tragic lines about hot alive Juliet looks before he drinks the poison to kill himself because he thinks she is dead.

She is just about to wake from her fake-death, and Romeo spends 30 lines or so in Act V, scene iii to tell her seemingly dead body how alive it actually looks. He notices the color coming back to her cheeks, the warmth of her body, and the beauty that has not been altered by Death's presence.

So he kisses her alive body and takes the poison to kill himself.

NOT THIRTY SECONDS LATER, Juliet wakes up wondering where Romeo is. Boy, that really stinks.

The greatest irony though is the fact that the hate between these two families was destroyed by true love.

Perhaps the best example of dramatic irony is at the very end of play, when Romeo believes Juliet is dead and then drinks the poison to end his own life. Dramatic irony occurs when the audience is aware of something the other character is not. In this case, we are aware that Juliet is not really dead but is merely awakening from the 42 hour slumber induced by Friar Lawrence's potion. Romeo, however, has not received the Friar's letter to inform him of this place and the Friar himself is too late to intervene.

One of the most moving or poignant (a quality of specialness) ironic moments in Shakespeare's Romeo and Juliet is when Romeo tries to stop Mercutio and Tybalt from fighting, but in the process gets Mercutio killed.

Romeo was probably never really a fighter, but since he's fallen in love with Juliet he wants the feud between the Montagues and the Capulets to stop.  He tries to get Mercutio and Tybalt to stop.  The problem is that the two skilled fighters are not really out to kill each other.  They are playing a game, though it's a very dangerous game.  But when Romeo comes between the two, an accident happens and Mercutio cannot protect himself.  And Mercutio dies.

This is powerfully ironic.  What's supposed to happen, doesn't.  What's supposed to stop the dying, causes it.