Here's another thumbs-up from a NOD32 user - it's very fast and there's no apparent limit to the AV signature update frequency (unlike Symantec's) either.

For spyware I too use AdAware and Spybot. While scanning customer's machines I sometimes use XoftSpy (subscription required) and, depending upon the direction of the wind, that catches important stuff that AdAware and Spybot misses - I think it's purely down to how often the signatures are updated.

One invaluable tool for checking running processes can be found at www.hijackthis.de - download and run the 'passive' checking tool and paste the results into the web form for an analysis.