There are many different styles of question which can be used very effectively to develop knowledge of mathematics and mathematical skill.

General use of interactive elements

A very simple tool is to allow the dragging of cards around on the screen. This device can be used in many ways.

IFFY logic  - This exercise gives practice in logical reasoning

Proof sorters - Proof sorters give students access to proofs beyond their means to construct directly, and can be used to transmit many mathematical ideas

Fluency and practice

There are many bad examples of this sort of thing on the web. Rather than simply use multiple choice, there are better ways to develop speed and fluency.

Mathmo

Problems making use of video

Video can be used effectively to set up a problem or activity

Summing geometric progressions

Sets of graded questions

Sometimes lots of small questions build up into a nice collection of structured exercises. These are good for allowing exploration of breaking down a difficult concept into more manageable chunks

Transformations for 10 

The clue is in the question 

Problems which consolidate learning

Some problems are ideal as end of topic consolidation or refreshment of ideas before a new topic is started.

Integration Matcher

Impossible triangles

Trig reps

Problems which introduce new ideas

Hyperbolic thinking

Problems which can be solved in many different ways

The same problems can often be solved in many different ways. This allows students to revisit problems when new content is learned.

Curved Square

Problems which may be used in multiple ways

The same problem can be used by a teacher in multiple ways, depending on the needs of the students. 

Whose line graph is it anyway?

Sequences of linked tasks and ideas

The web allows for tasks to be linked together in lots of interesting ways

Weekly Challenge 19: Prime Aps

Good contexts

Sometimes there is simply a great concept which can be used in many different ways

Power countdown

Calculus Countdown

General mathematical thinking

Some activities have relatively little content but can be good for developing mathematical thinking

Air nets

Painting by numbers

Interactive articles

Many expositions of material can be threaded with small questions along the way.

Euler's Formula and Topology

Introduction to differentiation

Problems allowing exposure to advanced mathematics

Often problems can be created which give access to the ideas involved in advanced mathematics, without the need for being able to do the advanced mathematics

Easy as abc

Just nice problems

There are lots of problems that are just nice to have around

Absurdity