Four lines rhyming AABB - scansion, rhythm, metre and all that malarkey is as random as-u-like. Oh yes - the featured subject, usually a person, is mentioned in the first line.
Here's a full and frank(ly better) intro by Thos along with some that were made earlier.
Expose more Expose all
Phil - Take That
Raak - Will get old and fat
penelope - Until relighting the fire
Kim - Is performed under their funeral pyre
Rosie - Laszlo Biro
Software - Perhaps inspired the Spanish artist Joan Miró
irach - While Walter A. Sheaffer
Raak - Supplied Jules Feiffer.
Software - Wendy Alexander
Rosie - Scratch-voiced gift demander
Raak - "Bring it on!" she said
CdM - And killed the game dead
And with, that, let us utter the magic Mornington Crescent words, for though Clerihews are always fun, this game has been running for a long long time, and it is time to shake things up around here.
Audience
*shouts, screams, generally goes wild for CdM*
Tuj - I think the audience should cheer for MC5 as a whole. This turned into a really good staple, long-running game.
Chalky - Shall we?

Julian Paul Assange
Software - Said "publish and be dammed"
penelope - But he didn't foresee
Rosie - What the outcome could be.
CdM - Chelsea Manning
Rosie - Now into fake tanning
Phil - Formerly Bradley,
Chalky - Self-styles badly.
CdM - Kevin Rudd
CdM - Too Australcentric? OK
Edward Snowden
penelope - Showed 'em
Raak - Too much information
Rosie - 'Bout his nation.
Software - David Miliband
Rosie - Unlike Blair, did not play in a silly band
Raak - His brother Ed
Phil - Should have been leader instead.
Rosie - Gareth Bale oblig.
Kim - Is beyond the pale [Raak] Steve, surely?
Software - With that amount of money
Rosie - His financial outlook could reasonably be described as sunny. revivalism...
Software - Bashar al-Assad
penelope - Had
Rosie - Some isopropyl methylphosphonofluoridate
Chalky - Which he used in manner profligate
Software - Vladmir Putin
Rosie - Hardly high-falutin' S. Wales pronunciation invoked.reveal
Phil - Is surprisingly camp reveal
This is the end of the line. There is no more.