How many trade offers can a villager have?

The maximum number of trade offers you can get a villager to generate will depend on their profession. Each time you trade the last (right-most) offer a villager has, two changes happen to their available trade offers:

• Any trade offers that have been used enough times to deactivate them will be reactivated.
• There is a chance that a new trade offer will be added to the end of their list, which will be a different item than the trade offers currently appearing. If no new offer is added it usually means a previous offer was reoffered at a new exchange rate (e.g. 20 wheat for an emerald changing to 19 wheat).

Therefore, if you haven't traded the last offer to the point of deactivation and the villager hasn't yet shown you all of their trade offers, there is still a chance for them to generate more. A list of the possible trade offers by profession can be found here. If you add them all up, you get the following for the maximum number of different trade offers a given villager type can possibly make as of version 1.6.4:

• Farmer: 14
• Librarian: 9
• Priest: 13
• Blacksmith: 26
• Butcher: 11

And I can confirm this is true for the Librarian, because I maxed one out already. ;)