There's always something which gives away a fake Rolex as exactly that. Counterfeiters never quite capture the character and features of a true example accurately. However, they sometimes overcompensate, trying to make something which looks more like a Rolex than a Rolex.
Things to notice:
1. The second hand stopping and starting for each second.
Genuine Rolexes have second hands which never stop moving for an instant.
2. The back of the watch is clear to show the workings.
Real Rolexes are always opaque at the back.
3. Engravings on back
True Rolex watches have no markings on the case backing (with two exceptions, see below). This is a prime example of overcompensation
4. The sticker the Rolex was first shipped with.
Genuine Rolexes have a 3D hologram-encoded in the sticker on the back. Fake ones just an unchanging logo or the word 'Rolex'.
5. The date the watch was made.
In 2002, the reference number was also changed from gold to black, and the Rolex crown logo appeared in the sticker for the first time, above the reference number.
6. A magnifying glass bubble to view the date in recent models.
Real Rolexes magnify the date by two to three times, whilst fake ones only make a tiny difference.
The only exceptions to the rule 3 about engravings on the back are: a few types of ladies' Rolexes from at least 15 years ago had 'Original Rolex Design' on the back, and Sea-Dweller watches have 'Rolex Oyster Original Gas Escape Valve'. Both have the engraving in an arc.
Rolex were naturally proud of their gas escape valve, which was designed with watchmakers Doxa, in watches used by divers. The valve released helium during decompression.
The above steps should help you pick real from rubbish, but of course it's always wise to buy from a reputable source.