Modern copies that are worth anything to a collector are very rare indeed...most are considered pure junk and despicable, especially if made to decieve. There is a series of well done fakes (imitations) called Paduan medals after Giovanni Cavino. 1500-1570 that are highly collectable and expensive because of their superb artistic style and beauty. These medals themselves are highly copied and faked and a real one is rather rare, most are after casts of the real series. Many would say Cavino was a medallist rather than a forger, an imitator giving homage and a true craftsman. In contrast to the crappy fakes that people try to pawn off as real.
Here are some examples of early after casts of paduan medals...

Paduan Medal of Galba

Paduan Medal of Domitian
Here is a worthless cheap copy of one of these medals that I own and bought in Rome:

These are bulgarian fakes...they are not that bad, but they are made by scum trying to pass them off as real...they are no Giovanni Cavino and they are worth the metal they are made of...they are worth nothing in my book save jail time.
http://www.cachecoins.org/coins/4.jpg^^ bulgarian fakes
Now there are people who do collect what are called Fourée. These coins are ancient fakes made contemporary (or closer) to the time of the coin they are faking. They are usualy made with a base metal and coated with silver (or another more precious metal). They often ashow breaks in the top layer if it remains at all. These are made to decieve by ancients but they are rather collectable as they are still ancient coins.
here is a few examples:

Otho Fourree

Roman Republic Mn. Fonteius silver denarius fourree 108-107 B.C.