I’m going to post here 6 years late, because I think this is a good question and I am not satisfied with the existing answers.
The static Parse/TryParse methods can be used only when you want to convert from string to the type that has those methods. (use TryParse when you expect that the conversion may fail).
The point of System.Convert is, as its documentation says, to convert from a base data type to another base data type. Note that with Convert you also have methods that take an Object and figure out by themselves how to convert it.
As to System.ComponentModel.TypeConverter, as the “typeconverter” stack overflow tag’s documentation, they are used primarily to convert to and from string, when you want to provide a text representation of a class instance for use by designer serialization or for display in property grids