Most of the free anti-spyware programs don't do anything until you actively run them. So, with those type of programs, it won't matter how many you have on your PC. e.g. if your programs are called A, B & C, you can run a scan with A, then one with B, followed by a scan with C, without any problems. The software won't be running simultaneously, so there's no chance of any conflicts occurring.
However, some of the newer programs (particularly the commercial versions) incorporate 'real-time scanning'. This means that, like your firewall and anti-virus software, they're running 'in the background' all of the time, checking everything which is downloaded to your PC. Having two of these programs on your PC might lead to conflicts, because they'd be trying to access the same data simultaneously.
The free AVG anti-spyware program works just like the full commercial program for the first 30 days (including 'real time scanning'). Thereafter, unless you pay to pay to upgrade to the commercial program, it reverts to being a basic 'run on demand program'. So, within the first 30 days, it would be unwise to install another program with real-time scanning.
The most popular free anti-spyware programs (which are both 'run on demand' programs) are Ad-Aware SE Personal and SpyBot Search & Destroy:
http://www.lavasoftusa.com/products/ad-aware_s e_personal.php
http://www.spybot.info/en/
Chris