Badlanders as the examples I promised: Dexim ad vs Jamie Nelson - This is what we call "demo love" - and what lawyers call "copyright infringement". and Double BLT magazine covers, NYT's "T" vs Coast a.k.a Toast.. This is not to be confused with obvious parodies that mimic a style on purpose to be funny. Like when John Cleese & Schweppes copied the style of CK perfume ads at the time.
Homages to other ads are a long-going tradition in UK advertising, but it's difficult to make them work in their own right so be careful with that.
The all time low is when ad agencies in far off lands re-use photographs they have no rights to use in their own ad campaigns, and this one tops them all as the mummy in that photograph is actually the copywriter of the original ad. When it comes to design you need to be inspired but watch out so it's not too inspired by all the great designers who came before you.
Clients will get in trouble for straight-up rip-offs. As they did in the case of Coke mimicking Joel Veitch's ninja kittens, and when Nike copied a chinese flash animators stick figures. These cases were won by the original creators, which is rare, but the bigger worry is when you piss off someone elses fanbase which may also be your customer base. Like when Nike copied Minor Theft or Jamba Juice borrowed heavily from Get Your War on. There is bigger danger in copying than simply being called a hack.