BusyBox is licensed under the GNU General Public License version 2 or later, which is generally abbreviated as the GPL. (This is the same license the Linux kernel is under, so you may be somewhat familiar with it by now.)
Anyone thinking of shipping BusyBox as part of a product should be familiar with the licensing terms under which they are allowed to use and distribute BusyBox. Read the full test of the GPL (either through the above link, or in the file LICENSE in the busybox tarball), and also read the Frequently Asked Questions about the GPL.
Basically, if you distribute GPL software the license requires that you also distribute the source code to that GPL-licensed software. So if you distribute BusyBox without making the source code to the version you distribute available, you violate the license terms, and thus infringe on the copyrights of BusyBox. (This requirement applies whether or not you modified BusyBox; either way the license terms still apply to you.) Read the license text for the details.
BusyBox's copyrights are enforced by the Software Freedom Law Center, which "accepts primary responsibility for enforcement of US copyrights on the software... and coordinates international copyright enforcement efforts for such works as necessary." If you distribute BusyBox in a way that doesn't comply with the terms of the license BusyBox is distributed under, expect to hear from these guys. Their entire reason for existing is to do pro-bono legal work for free/open source software projects. (We used to list people who violate the BusyBox license in The Hall of Shame, but these days we find it much more effective to hand them over to the lawyers.)
Our enforcement efforts are aimed at bringing people into compliance with the BusyBox license. Open source software is under a different license from proprietary software, but if you violate that license you're still a software pirate and the law gives the vendor (us) some big sticks to play with. We don't want monetary awards, injunctions, or to generate bad PR for a company, unless that's the only way to get somebody that repeatedly ignores us to comply with the license on our code.
These days, Linksys is doing a good job at complying with the GPL, they get to be an example of how to do things right. Please take a moment and check out what they do with distributing the firmware for their WRT54G Router. Following their example would be a fine way to ensure that you have also fulfilled your licensing obligations.