Mcafee, hands down, finds more trojan and spy ware than any AV i've used. You just have to turn on the setting to detect "potentially unwated and joke programs"
To answer your question, Properly configured, you do not need all of the software you run, however each is specialized, none of wh
at you listed really over-laps in functions.
Ad-aware is going to look at your cookies and registry, installed programs and look for "spy-ware"
Norton, is going to look for infections from trojan's and viri- not really the same a spy-ware in most cases... (qhost virus is a bit of both viri+spy-ware)
ZoneAlarm PRO does have a little bit of Anti-virus built-in now, with it's Email scanning. but not much else, and it is mainly looking for known code that will execute maliciously. ZAP, is a Firewall and Process monitor first, a cookie blocker and AV product second. Very little over laps here. Spy-bot and ad-aware a very similar, but still different.
The firewall on a router from a dsl/cable provider is typically not as good as you need these days. ZA will server you well if configured correctly.
McAfee always surprises me, I do security for clients, and I download tools all the time for testing and use, and McAfee On-Access scan catches ton's of the tools I am trying to DL becuse they indeed can have a malicious purpose, that's why I want them. Norton doesn't do it for me, and I've not tested any other's besides the big 2, mcafee and norton.
Mcafee catches all the password crackers I know about, all the key logging, even the ones sold to parents to spy on their children, etc...
Schedule regular updates, and daily scans of all your HD's