There isn't a limit to how many Analytics events you can send in total, but there are a couple of things to keep in mind.
- There is a limit on the number of events per player per day of 10,000, this far exceeds the number of events that are required to obatin a really rich understanding of the player's in-game behaviour. If a player exceeds this total any further events will be discarded until their event counter resets the following day. This measure is intended to prevent your dataset being polluted with events that are most likely not useful or valid.
- Unity Analytics follows a metered billing model with tiered pricing based on the number of Monthly Active Users (MAU) that the game has. On top of this there is a fair usage model for an average of 500 custom events per MAU, exceeding this be subject to a fair usage surcharge proportional to the excess. Having said that, fair usage limits do not apply to projects that are within the Free Tier of Unity Analytics.
For more information, see documentation on Unity Analytics and MAU Based Pricing