I find the GIMP is very good at making animated gifs, and for optimising them so their file sizes are small too. You just put each frame of the animation in a different layer, starting with the bottom layer for frame one, then when you choose to save as a gif, tell it to save as an animation rather than flatten the layers. You can also control how it animates from frame to frame e.g. speed by adding certain keywords into the names of each frame.