Interesting question!

The other replies so far have included some really interesting ideas. I'd like to focus on a few others here.

The answer, I think, lies in the perception of 'the public' - that is, a large community of people aware of one another, connected under a shared national identity and culture.

To elaborate - the reason you don't see much in the way of widespread, organised protest in many European countries before the sixteenth century is twofold. The first reason lies with the fact that it's fairly inaccurate to talk about a 'public' (as above) before this period. Typically, countries like England had started the processes involved in the bureaucratic centralisation of power by this time, but regional authorities still maintained a significant level of influence and personal control - that is, local nobility continued to represent the main authority for people in provincial areas.

What's the point of all this? Well, simply: as a peasant in early-Tudor England, you live in what might be termed (a little inaccurately) a 'mini-kingdom'. That's a bit of an oversimplification, but what it means is that you really aren't all that influenced by what's happening in other mini-kingdoms.

The second is the lack of an organised and effective method of information dissemination. National 'news' didn't really gather much momentum in England until around 1665 with the Oxford Gazette (though 'corantos' and newsbooks had been fairly popular in the capital periodically since the 1620s). In order to stimulate a widespread reaction to an event (a protest), people need to experience the news at a relatively similar time, with knowledge of how other people are reacting too. Word of mouth might pass news along, but it's an eventual process - sporadic, and disorganised.

Only when there was more cohesion between the 'public', and the means for people to experience an event at the same time, do we see a popular reaction take place. Example - the 'Popish Plot' and 'Exclusion Crisis' in England saw a popular reaction, stimulated in part by the widespread dissemination of news and the 'community of the mind' that had sprung up as the public formed.

A small caveat - this isn't always true, of course. In History, nothing ever is. Popular uprisings did take place before then (the German Peasants' Revolt, for example), but I think this is why you see it much more after the 1600s, as your question asks.

For more information: see Jurgen Habermas's very well-known Structural Transformation of the Public Sphere and Benedict Anderson's Imagined Communities.