When it comes to the decision between let and const (both block scoped), always prefer const so that the usage is clear in the code. That way, if you try to redeclare the variable, you'll get an error. If there's no other choice but redeclare it, just switch for let. Note that, as Anthony says, the const values aren't immutable (for instances, a const object can have properties mutated).
When it comes to var, since ES6 is out, I never used it in production code and can't think of a use case for it. One point that might consider one to use it is JavaScript hosting - while let and const are not hoisted, var declaration is. Yet, beware that variables declared with var have a function scope, not a block scope («if declared outside any function, they will be globally available throughout the program; if declared within a function, they are only available within the function itself», in HackerRank - Variable Declaration Keywords). You can think of let as the block scoped version of var.