I don't always love Aristophanes; he can really cram the obscure contemporary references into his stuff, which makes it sortof impossible to get the jokes. But he makes a lot of fart jokes, too, and those are timeless.
In order, the best of these plays:
1) Lysistrata, by a long shot. The most original of Aristophanes' ideas, and the most timeless: as recently as 2012, feminists sarcastically suggested a Lysistrata when the Republicans accidentally launched an ill-fated war on birth control. The story is that Athenian women conspire with Spartans to deny sex to their husbands until they end the war. That idea is simple, funny and filthy. (This is, depending on your translation, the first time dildos are mentioned in literature.)
2) The Birds, which I like to imagine animated in the Yellow Submarine style. Clean and well thought out.
3) Clouds, relevant because it's about Socrates, whom we know, and because it includes the best of Aristophanes' fart jokes - which is saying something since, as noted above, Aristophanes really likes fart jokes.
4) Frogs, which is mainly an argument between Aeschylus and Euripides about who's the best dramatist. (The play up til that climactic confrontation, which describes Dionysos disguised as Herakles journeying to the underworld to find a great poet, is faintly amusing but largely forgettable.) Aristophanes leaves Sophocles out, claiming that he's too dignified to bother with the whole charade (although one has to imagine that, however sweetly it's explained away, his absence has to betray Aristophanes' judgment). This was a lot of fun for me - and it's getting the most time here because I'm reading it right now, and realizing as I do that I never really reviewed the rest of them; I've done my best to write capsule reviews of those, but they're not what I'm thinking of at this moment. Anyway, I can't see the attraction for anyone who isn't pretty invested in both Aeschylus and Euripides. It contains what amounts to scholarly comparison of the metres of both poets; at times it sounds like a grad thesis.
Aeschylus appears to come out the winner here, but it does seems like all the best lines go to Euripides. Maybe this is just my own prejudice coloring my interpretation; I like Aeschylus, but I like the enfant terrible,
tricky and rebellious Euripides better. To me, Aeschylus comes out pretty stodgy.
Aeschylus: The poet should cover up scandal, and not let anyone see it.
Euripides: You ought to make the people talk like people!
This judgment by the Chorus seems about accurate:
One [Aeschylus] is a wrestler strong and tough;
quick the other one [Euripides], deft in defensive throws and the back-heel stuff.
And at the last, after Aeschylus has beaten Euripides, line for line, Dionysos says:
One of them's a great poet, I like the other one.
I'm going to go ahead and decide Aristophanes secretly agrees with me: Euripides is more fun. (Note: the text really doesn't support my conclusion.)
Aristophanes is aiming at, and concludes with, a more serious question for his time: should the politician Alcibiades be followed? Aeschylus says yes, Euripides says no. This is during the Peloponnesian War between Athens and Greece. Alcibiades, a politician with an amazing capacity for joining whichever side happened to be winning - he had switched from Athens to Sparta to Persia back to Athens - would soon be exiled after some disastrous naval losses. (And Athens will, y'know, lose this war.) Aristophanes didn't know this yet (if I have the dates right here), but Euripides was right.