I've put together a short list of things that rhyme with hug me for those of you that were stuck on this one.
Bug Bee - That bug is a bee
Chug Gee - There is Dolly the chug, gee.
Doug Be - Doug be all over the place today, he's crazy.
Drug Free - The correct way if we are talking illegal substances
Dug Oui - Can I get that dug? Oui
Jug Key - The key, for the jug.
Lug Pee - Something no one wants to do.
Mug Pea - The Pea, for the mug.
Plug Lee (in) - To charge him up.
Pug Plea - A plea from all the pugs out there, with their cute little faces.
Rug See - It's a rug, see.
Shrug Spree - What you can't get enough of shrugging.
Slug He - That slug is a male
Smug Sea - No one likes when the sea is smug, with it's waves and it's lapping on the shore.
Snug Ski - This ski fits lovely
Thug She - A female thug
Tug Tee - When your tee is stuck in the grass, tug it.
oh and I want to add this one. Puffy!!
Puffy rhymes with hug me!
As does ritzy.