BusyBox is licensed under the GNU General Public License version 2, which is often abbreviated as GPLv2. (This is the same license the Linux kernel is under, so you may be somewhat familiar with it by now.)
A complete copy of the license text is included in the file LICENSE in the BusyBox source code.
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.
Version 2 of the GPL is the only version of the GPL which current versions of BusyBox may be distributed under. New code added to the tree is licensed GPL version 2, and the project's license is GPL version 2.
Older versions of BusyBox (versions 1.2.2 and earlier, up through about svn 16112) included variants of the recommended "GPL version 2 or (at your option) later versions" boilerplate permission grant. Ancient versions of BusyBox (before svn 49) did not specify any version at all, and section 9 of GPLv2 (the most recent version at the time) says those old versions may be redistributed under any version of GPL (including the obsolete V1). This was conceptually similar to a dual license, except that the different licenses were different versions of the GPL.
However, BusyBox has apparently always contained chunks of code that were licensed under GPL version 2 only. Examples include applets written by Linus Torvalds (util-linux/mkfs_minix.c and util_linux/mkswap.c) which stated they "may be redistributed as per the Linux copyright" (which Linus clarified in the 2.4.0-pre8 release announcement in 2000 was GPLv2 only), and Linux kernel code copied into libbb/loop.c (after Linus's announcement). There are probably more, because all we used to check was that the code was GPL, not which version. (Before the GPLv3 draft proceedings in 2006, it was a purely theoretical issue that didn't come up much.)
To summarize: every version of BusyBox may be distributed under the terms of GPL version 2. New versions (after 1.2.2) may only be distributed under GPLv2, not under other versions of the GPL. Older versions of BusyBox might (or might not) be distributable under other versions of the GPL. If you want to use a GPL version other than 2, you should start with one of the old versions such as release 1.2.2 or SVN 16112, and do your own homework to identify and remove any code that can't be licensed under the GPL version you want to use. New development is all GPLv2.
BusyBox's copyrights are enforced by the Software Freedom Law Center (you can contact them at firstname.lastname@example.org), 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.