How can I have my Mac auto-connect to my wifi network?

The issue you're talking about is related to what Mac OS X calls a preferred network. Depending on how you have things configured, your Mac might well only connect to those networks you've specified as preferred. Generally, any network you access succesfully should be on that list, but I have seen that sometimes it doesn't work. My sneaking suspicion is that it's something to do with 802.11b versus 802.11g networks, but I have no actual data to prove my case. :-)

Let me show you how to specify that a given network is a preferred wireless network, however, and you can go from there...

Start out with Apple --> System Preferences... and choose Network. Most likely, it'll look like this:

If you have something else, no worries. What you want to do is specify Automatic for Location and Airport for Show. Now it'll look like this:

You can see that I have "By default, join Preferred networks", the other choice is "automatic", but given your description, I'm betting yours is set similarly.

Below that is a list of preferred networks, including Aerie, AngelNet, Steve Hardesty, Angelnet and quite a few more. Frankly, you can see where I use my laptop based on the names of the networks I have on this list!

To change a preferred network connection, select it and click "Edit", and do remove one that you no longer want to have on your preferred (auto-connect) list, simply delete it from the list by selecting it and clicking on the "-" button.

To add a new preferred network, click on "+" and you'll see:

Type in the name (SSID, base station ID, whatever you want to call it) of the network you want to join, then specify the correct security, if any. If the network does use some sort of password scheme, you'll be promoted for the network access password too: type that in, click "OK" and you should now have a new preferred network on the list, the network you want to be able to automatically join whenever it's detected.