Personally, I run nothing but the SP2 firewall on my PC and my wife's. However, it is only an 'inbound' type firewall, whereas the others you mention are two way, inbound and outbound. They are also 'rules-based' in that you can choose what applications, etc. have 'Net access.
If you do decide to use one of them, disable the SP2 firewall (after disconnecting from the 'Net first!).
I have use Sygate before with no problems.

If you have some antivirus software running and are current on windows updates then SP2's firewall should be more than fine.  While the 3rd party firewalls you mention do offer "outbound" protect I have personally never benefited from that feature.  If you are careless about what you download and run, like opening random email attachments and the like, then perhaps you should get one.  If you are more careful, you should be fine.

I have used sygate and zone alarm before and I think sygate is much to be preferred.

Also, the easiest way to protect your computer is not to log into an administrative account unless you absolutely have to.  Do the web-surfing and the like on a limited account and you'll be much more protected

Just to complete the range of available opinions: I use ZA free and find it useful, yet simple to use to control outbound connection.

I finally installed SP2 after doing all the puter tweaks that I saw recommmended around the web. From what I understand, the original XP had a firewall, but you had to turn it on. It has to be turned off

If the firewall was not on post-SP2, then the new Security Center would have warned you about this on the first reboot.

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@lmfbr wrote:
I have the XP firewall running and no other firewall installed. Would I be better off by turning the XP firewall off and installing the free version of Sygate or the free version of Zone Alarm (if they are still free)?

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