All the tutorials here and advice elsewhere...seem to assume (am I wrong here?) you've got nothing on the computer, so the suggestions are to install this and scan, install that and scan ... fine and good when starting from from a filthy, unprotected jungle of a computer.
When we are helping users with malware removal, we often suggest downloading various anti-malware scanning tools like Ad-Aware, Spybot, Ewido, and sometimes trials like Counterspy, Spysweeper etc. even if they have another scanning tool. The only problem that I have encounterd is that some of these tools can interfere with various fixes (removal instructions). When that is the case, I simply advise the victim to temporarily disable it.
I suppose there can be performance issues with those that are resource heavy and there can be a point of overkill by using too many. But I'm not aware of any incompatabilty issues with using several of the well known programs together. Thats not to say this is always the case, just that I have not encountered a problem.
Anti-virus programs are another matter. You can have more than one anti-virus program installed on your system as long as only one of them is actively running and providing real time protection. The other should only be used as an on demand scanner. However, even when one of them is not running, problems can still arise when the active anti-virus detects the non-active one's definitions or quarantined files.
The concern with using more than one anti-virus program is due to conflicts that can arise from them both running together at the same time in real-time protection mode. Anti-virus software componets insert themselves into the operating systems core and using more than one can cause instability, crash your computer, slow performance and waste system resources. When actively running in the background while connected to the Internet, they both may try to update their defintion databases are the same time. As the programs compete for resources required to download the necessary files this often can result in sluggish system performance.
While operating in real-time mode, each program will often interpret the activity of the other as a virus and there is a greater chance of them alerting you to "False Positives". Further, if one AV finds a virus and then the other also finds the same virus, then both programs will be competing over exclusive rights on dealing with that virus. Each piece of AV software will attempt to seize the offending file and quarantine it. If one AV finds and quarantines the file before the other one does, then you encounter the problem of both AV's wanting to scan each other's zipped or archived files and each reporting the other's quarantined contents. This can lead to a repetivite cycle of endless alerts that continually warn you that a virus has been found.