It looks to me like you are suffering from a lack of anti-aliasing.
If you are using cycles, you'll need more than one sample (Properties > Render > Sampling) in order to get good anti-aliasing. Try maybe 15 or so, and increase until the result is smooth enough for your liking.
Keep an eye on the rendertime though.
If your animation consists entirely of flat colors, I would recommend using BI or
OpenGL render instead.
The OpenGL render operates using the same techniques for the viewport and realtime games. In other words, it renders nearly instantaneously (especially for flat colors).
To enable anti-aliasing when using OpenGL render, enable Anti-Aliasing in Info > Render > OpenGL options and choose a suitable number of AA samples (more == slower but smoother):
If you need a little more than just flat colors (motion blur, for instance), then you might consider BI. While perhaps slower than OpenGL (depending on your hardware), it's still much faster than Cycles when it comes to flat shading: