I installed Tiger onto my Lenny box, and it gives me the following warnings repeatedly:

"The process `avahi-daemon' is listening on socket 52636" (or other numbers)
"The process `rpc.statd' is listening on socket 34157" (or other numbers)

Should I be concerned? Is it time to declare my computer a security risk and detonate it with dynamite immediately?

I would suggest you instead determine whether you need/want Avahi and/or RPC. If you don't, then you can always remove them (no high explosives necessary). I think the Avahi package is called avahi-daemon and RPC is provided by portmap, which is a dependency of both NFS and NIS.

I think libsane depends on avahi, and I've a scanner. I may get rid of portmap, but I'm worried that mount indirectly relies upon it.

Anyway, from what I understand, these are not unusual programs. Why is Tiger making a fuss over them?

It's just objectively listing what's going on. Determining something to be benign or malicious is left to human interpretation.

It depends on the library, not the daemon (look here).

Unless you've got clients that make use of that service, you don't need it. If you don't want to remove the package, keep in mind you could instead just make it so that it doesn't get automatically loaded at startup time (the same could be said for the Avahi daemon).

unSpawn: Objectively? It seems that flagging something with a big all-capitals "WARN" is hardly objective. Plus, it's not listing all processes; rather, it's being selective in that which it warns about. Granted, though, it did not accord the status of "FAIL" to the aforementioned processes, so perhaps they're not something that need raise too much concern.

win32sux: when in doubt, throw it out. Be free of unnecessary clutter. So, gone are portmap and avahi-daemon, along with a few others. Time to reboot and see if the machine has survived this surgery.

[later] Well, the reboot was a success. It'll be interesting to discover if I've lost any functionality from the recent removals.