I've been attending the Oregon Shakespeare Festival for 45 years. Not every year, certainly, but often enough. And I've sought out other productions. I saw Cymbeline and The Two Noble Kinsmen on a recent trip to England, for instance. There may be a couple minor ones I've missed (Troilus and Cressida? I can't recall offhand whether I've seen that), but aside from that I've seen staged productions of every play Shakespeare wrote. The lesser-known plays that most impressed me with the dynamite of a good performance were Coriolanus and the Henry VI trilogy, all at OSF. But then I've seen good productions of almost everything, even Pericles. Also at OSF.
Aside from my period in a Shakespeare reading group at the public library, however, I've almost never sat down and read one of his plays from end to end. Drama is for seeing on stage, not reading in the armchair. Tolkien held it to be a distinctive art form from literature (fiction and poetry), not as an insult but as a principle of classification, and even though it's often written by the same people, I agree. I feel the same way about opera vs. concert music.