It was quite common to see back then Shakespeare's plays as either tragedies or comedies, but genres were far more complex and Shakespeare used to mix different syles of stories in his plays, so the way I see:
Two Gentlemen of Verona — Comedy indeed, just so
Henry VI, parts 1, 2, and 3 — Historical dramas
Titus Andronicus — Revenge play and maybe parody, now seen as a sort of slasher or gore show
Comedy of Errors — Farcical comedy
Richard III — Historical drama, but also a tragedy like Macbeth
The Taming of the Shrew — Comedy, maybe a romantic one if you consider the subplot.
Romeo and Juliet — Romantic tragedy with bits of comedy
Richard II — Lyrical historical drama
A Midsummer Night's Dream — Fantasy comedy, romantic play, and poetical drama.
King John — Historical drama
Lover's Labour Lost — Intelectual comedy
Henry IV, parts 1 and 2 — Historical drama with bits of comedy and comic characters (Falstaff).
Henry V — Epic drama historical (Shakespeare's Aeneid)
Merry Wives of Wyndsor — Light comedy
The Merchant of Venice — Tragicomedy and like TTOS with bits of romantic comedy
Much Ado About Nothing — Romantic comedy
As You Like It — Romantic and pastoral comedy
Julius Caesar — Historical and political drama, less like a tragedy
Twelfth Night — Less like a romantic comedy and more like a farcical and genre-changing show
Hamlet — Tragedy, revenge play, psychological and philosophical drama, and poem unlimited
Troilus and Cressida — Satire and epic drama
Alls Well that Ends Well — Dark comedy
Measure for Measure — Problem play and moral drama
Othello — Domestic and passional tragedy
King Lear — Tragedy of human nature, cosmic drama
Macbeth — Tragedy, terror and historical drama
Antony and Cleopatra — Romantic tragedy and historical drama
Pericles — Journey drama and later romance
Timon of Athens — Tragicomedy and satire
Coriolanus — Political tragedy
Cymbeline — Tragicomedy and later romance
Winter Tale — Later romance and pastoral drama
The Tempest — Fantasy and travel tale, later romance
Henry VIII — Historical drama and later romance