What does this mean for Avahi? First of all although the Apache License is much better than the APSL it still isn't GPL compatible (at least in the eyes of the FSF), which effectively means that Bonjour still cannot be used by more than 66% of the Free Software projects available. Secondly Avahi is more powerful in most areas than Bonjour ever was. (In fact, there is only a single feature where Bonjour surpasses us: writable "Wide Area DNS-SD"). Avahi uses all the "hot" Free technologies like D-Bus and a has much better integration in the Linux networking subsystem. Avahi is more secure (chroot()...) Avahi is compatible API- and ABI-wise with Bonjour, but not the other way round. Avahi is now part of every major Linux distribution.
Avahi is actively developed. The aforementioned Wide Area DNS-SD is currently being worked on by Federico Lucifredi. Since I will write my master thesis about mDNS scalability a lot of additional development will be done for Avahi in the next month.
In short: Avahi is here to stay. Apple's move to the Apache license is too little, too late.
Update: the Bonjour client libraries are BSD licensed, so the 66% argument doesn't hold.