Generally to detect collisions in canvas games I use something like:

function collides(a, b) {
   return a.x < b.x + b.width &&
     a.x + a.width > b.x &&
     a.y < b.y + b.height &&
     a.y + a.height > b.y;
}

But this only detects collisions if the objects are touching at the time the frame is processed. If I have a sprite whose speed (in pixels/frame) is greater than the width of an obstacle in its path, it will pass through the obstacle without the collision being detected.

How would I go about checking what's in between the sprite and its destination?

Edit
Report