2018 update:

There is now a stage 3 proposal – I am looking forward to make this answer obsolete in a few months.

In the meantime anyone using TypeScript or babel can use the syntax:

varName = value

Inside a class declaration/expression body and it will define a variable. Hopefully in a few months/weeks I’ll be able to post an update.

Update: Chrome 74 now ships with this syntax working.

The notes in the ES wiki for the proposal in ES6 (maximally minimal classes) note:

There is (intentionally) no direct declarative way to define either prototype data properties (other than methods) class properties, or instance property

Class properties and prototype data properties need be created outside the declaration.

Properties specified in a class definition are assigned the same attributes as if they appeared in an object literal.

This means that what you’re asking for was considered, and explicitly decided against.

but… why?

Good question. The good people of TC39 want class declarations to declare and define the capabilities of a class. Not its members. An ES6 class declaration defines its contract for its user.

Remember, a class definition defines prototype methods – defining variables on the prototype is generally not something you do.
You can, of course use:

    this.foo = bar

In the constructor like you suggested. Also see the summary of the consensus.

ES7 and beyond

A new proposal for ES7 is being worked on that allows more concise instance variables through class declarations and expressions – https://esdiscuss.org/topic/es7-property-initializers