I have seen your game samples. In this specific case I would use a grid. Divide the game screen into squares. Create a 2D-Array representing the game screen squares and containing reference to the game objects inside each square (2d array of object lists).
Check for collisions between all the objects that are inside the same squares (that can collide with one another). An average sized object can be in up to four squares at most.
Update the 2d-array every time you move an object. The object 'remembers' in which squares it is, so you only need to update 8 squares at most even if the object teleports away.