Well, I have seen AVG Anti-Spyware miss something while A-Squared Free catching more while doing an on-demand scan. It was on my sister's computer.
Anyway ... While that did happen, Yahoo! Toolbar's intergrated Norton Antispyware (which hasn't been updated in a while) caught another something else while Ad-Aware and Spybot Search & Destroy didn't (and their on-demand scanning is great). I can't recall what infected files they were, but that was a funny thing.
Well, this proves too much security (as long as not conflicting resident scanning) can't be too bad. I recommend both A-Squared and AVG Anti-Spyware, but you definatly don't need them both. Try them out, and take a look on how you like the features, interface, and preformance. On the side note, AVG AS has a 30 trial period (with resident scanning) and after it gets into a limited free version, without resident scanning, and then isn't any different from A-Squared Free.
----Also, you may consider a worthy resident scanner antispyware program. I find that it helps in certain situations.