The idea behind SSID On is the fear of uniformed users that if the Wireless is broadcasting and thus its existence of the Access Point appears on someone else available Wireless Networks, it might encourage someone to try to break the Wireless security.
Thus far WPA was Not broken and I doubt that if any one secretly knows how brake it his choice would be to brake into Joe Six Pack from Main street USA Wireless Network.
One can alose assume that any one that know how to deal with encryption codes can sniff Wireless beacon even if the SSID is Off.
On the other hand Entry level Wireless systems are Not stable when the SSID is off.
----------
From the weakest to the strongest, Wireless security capacity is.
No Security
Switching Off SSID (same has No Security. SSID can be easily sniffed even if it is Off)
MAC Filtering______(Band Aid if nothing else is available, MAC number can be easily Spoofed).
WEP64____(Easy, to "Break" by knowledgeable people).
WEP128___(A little Harder, but "Hackable" too).
-------------------
The above, are Not considered safe.
Safe Starts here with WPA.
-------------------
WPA-PSK__(Very Hard to Break).
WPA-AES__(Not functionally Breakable)
WPA2____ (Not functionally Breakable).
Note 1: WPA-AES the the current entry level rendition of WPA2.
Note 2: If you use WinXP bellow SP3 and did not updated it, you would have to download the WPA2 patch from Microsoft. <
http://support.microsoft.com/kb/893357>
The documentation of your Wireless devices (Wireless Router, and Wireless Computer's Card) should state the type of security that is available with your Wireless hardware.
All devices MUST be set to the same security level using the same pass phrase.
Therefore the security must be set according what ever is the best possible of one of the Wireless devices.
I.e. even if most of your system might be capable to be configured to the max. with WPA2, but one device is only capable to be configured to max . of WEP, to whole system must be configured to WEP.
If you need more good security and one device (like a Wireless card that can do WEP only) is holding better security for the whole Network, replace the device with a better one.
Setting Wireless Security - <
http://www.ezlan.net/Wireless_Security.html>
The Core differences between WEP, WPA, and WPA2 - <
http://www.ezlan.net/wpa_wep.html>