Anti Spyware programs

No, you can run both, one after the other.

One program may detect spyware in the other's quarantine but other than that there shouldn't be any other problems.

Agreed. I run Windows Defender and Spybot S&D in parallel - no problems.

Thanks.

I'd also put the free version of AVG Antispyware on - it used to be Ewido - as it's one of the best

Cheers. Done that too.

I used Ad-aware for years but didn't really like the latest version so switched to the AVG one. Like it so far.

Two more really good free scanners (pay resident option available.)
IMO at least as good as AVG, and a bit better than Adaware.
They might be better than Spybot, too, but I just won't say a bad word about 'ole faithfull.

I have the usual (AdAware, Spybot, AVG) - do I really need more to ensure my computer stays clean?

AdAware personal (se) will no longer be supported in the next few months, as AdAware 2007 has replaced it. Some users are of the opinion that it's not that good.
Spybot is getting pretty dated, though still useful, and the forums are (apparently) good, and helpful.
AVG AS (if it's AS and not AV you're meaning) is the only "state of the art" scanner you have. So I would say it would be wise to install another State of the art one, to be sure.
Either SAS or Asquared.
Depends how risky or careless a user you are, and what order of protection you need. Eg: if you are doing cc transactions online, then, yes, it's important.