So, there is no correct answer to this question.

Traditional doctrine said about 3 bases (80-90 Probes).  This is necessary to continue adding to the standard Protoss "death ball" out of 6 Gate + 2 Robo, while adding in HT.  Supporting your death ball requires at least 2 bases in mid to late game, and to make the tech transition to HT on 2 base is usually a blunder which will cost you the game.  So if you're going for the standard Colossus into HT, you have to have that third base saturated.


More recently, high end Protoss players (oGsMC), have been moving away from the classic Colossus into High Templar and have been moving towards even heavier economic builds (like Colossus Void Ray).  Whether these are strategies which favor the more macro centric 1 Gate Expanding Protoss, or responses to the new Kadaren Amulet nerf (which was announced weeks ago), we're now seeing Protoss players getting 110+ Probes on 4 Bases.

Ultimately how many Probes you build is a function of what your timing windows are.  The question should never be: *How many Probes do I build?*  Rather the question you should be asking is **When do I stop building Probes?**

Knowing when to cut Probe production is a skill, and that timing is what makes your BO effective