If your connection is working fine, you probably have both a Wired and Wireless NIC. It's only showing an X because 1 of those 2 aren't working. At least this is what makes sense to me especially if you're able to get online. It doesn't mean it's broken per say, just means one isn't connected. If this doesn't seem like the problem, post back and give more info. (Why do you think somethings wrong if it's working etc...)

ViennaPro is correct, it seems as though you have the two network connections enabled (both wired and wireless)

If you do not wish to see the red cross on the task bar, you could always disable your wired network connection. (right click on the connection and click 'disable' in the mangage network connections window)

Hi I had the same prob with windows 7, my internet connection was working fine, the connection/signal bar was showing my wireless signal strength, all good until i bridged the connection so i can use my ps3 online.
After that there was always a red cross on the signal bars but the internet was working fine. Even when the ps3 was connected the cross was still there. When i removed the bridge no red cross. So if you have a bridged connection that may be the prob.
My advise to you is that if the internet works fine & you dont have any probs going online then leave it alone, who cares about the cross, important thing is you can still use the internet.
Hope that helped