In your Stroke palette, set Cap to Round and Join to Round (with the object selected). Also, I think in CS2 you can make adjustments to the Mitre Limit of a join, this will also adjust the spikes.
One more thing - Sometimes this 'spiking' is caused by unnecessary points near the join, check it out.
I hope this comes close to answering your question.
Making the Miter Limit a smaller number will remove spikes, but Vintendo's first suggestion is the best of changing the join and the cap to round.
If you are making logos like this with multiple strokes, it is best to use the appearance pallette to add multiple strokes to one path. A lot easier to do revisions adn more contorl once you master the appearance palette.