This is exactly the opposite of what many security experts recommend: ideally all devices should be secure regardless of whether the network they're on is secure or not. With more and more devices offering remote-Internet-access functionality every day, this principle of security is becoming ever more fundamental.
Bruce Schneier's personal WiFi network at home is fully open, because -- in his own words: "If I configure my computer to be secure regardless of the network it's on, then it simply doesn't matter. And if my computer isn't secure on a public network, securing my own network isn't going to reduce my risk very much."[1]
Like rachelbythebay, I'm also waiting for the great network printer security apocalypse.[2]
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[1] http://www.schneier.com/blog/archives/2008/01/my_open_wirele...
[2] http://news.ycombinator.com/item?id=4412522
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UPDATE: Just for the heck of it, I ran a fairly fast scan (nmap -T4 -A -v -PE [IP address]) on an HP all-in-one printer accessible over my LAN, and there were a LOT of open ports -- see pasted results below. I then pointed my browser to port 9100 on the printer, which instantly printed the HTTP headers without complaint. The printer's configuration page reports that it is "secured" by an administrative password.
PORT STATE SERVICE VERSION
80/tcp open http HP PhotoSmart/Deskjet printer http config (Virata embedded httpd 6_0_1)
139/tcp open netbios-ssn?
6839/tcp open tcpwrapped
7435/tcp open tcpwrapped
8089/tcp open tcpwrapped
9100/tcp open jetdirect?
9101/tcp open jetdirect?
9102/tcp open jetdirect?
9110/tcp open unknown
9220/tcp open hp-gsg HP Generic Scan Gateway 1.0
9290/tcp open hp-gsg IEEE 1284.4 scan peripheral gateway
9500/tcp open unknown