I think some people see it as a measure of their value as a professional. If you have 500+ connections, then you've obviously been around and know everyone. This impression can increase your commercial value when you're looking for executive or sales positions. Business is fundamentally social, and if you can leverage a large network in favor of your employer, you become much more valuable than a smooth talker with no connections.

It does kind of ruin the "introduce me" featureset when everyone you contact is going to say "Actually, err, I can't introduce you guys because I don't actually know him", though.

LinkedIn should mitigate this by minimizing or not even displaying the "number of connections" on profiles and emphasizing other value measurements that don't cause misaligned incentives.