How can I find out what Wifi networks my iPhone knows about?

Where there's a will there's a way ;)

From a stock iPhone this is not possible from the settings. The information that you want is stored in the iPhone's keychain. If you have access to the iPhone SDK you can start messing around if you like, but I will leave it at that since that would be a StackOverflow answer.

Exact location is: /private/var/Keychains/keychain-2.db

I think the only way is to actually be in range of the network that you want to get rid of. You can't actually see what networks you have stored, not that I know of, but if you want to get rid of a network.

Settings > Wifi >

Then select the blue arrow on the right of the network that you are connected to and click "Forget this Network"

If you are not interested to find out the algorhythm used to pick the network but only want to view the list of remembered networks, there are at least three Cydia apps: "wifi passwords", "networkknowledge" and "networklist".

(The first has the advantage that it is a standalone app and does not install a mobilesubstrate library, while the others have the advantage that display the information right where you expect it in the wifi settings but at the cost of bulking the device with yet another mobilesubstrate library)

Bonus, this will also show the stored passwords in cleartext!
You will need to jailbreak the device first though, since access to the needed information require root privileges.

There is a way to do this without jail-breaking your iPhone.

1) First you need to download a program called "Cydia Impactor". -Link:http://www.cydiaimpactor.com/

2) Next, download what's called the 'ipa' file of either one of a 3rd party Cydia apps called "networklist". -Link: http://idroidnews.net/networklist-cydia-tweak-to-view-list-saved-wifi-passwords-in-settings.html

3) Run Impactor.exe and connect your iPhone to your computer via USB cable.

4) The program should display your phone's information, indicating that it recognizes the device. Now simply drag the .ipa file onto your phone's name.

5) The program will then ask for your AppleID and password. *Do not worry. The program does not collect password information, and you can also use any other valid AppleID w/password, it does not matter.

6) The way the program works is that it uses your AppleID to apply for a free, 7-day developer certificate, essentially it makes you a valid developer just like TUTUapp or IOSemus.

7) *Do not try to open up the newly installed app on your phone yet, it won't work until you trust the developer. Go to your Settings>General>Profiles and you should see your AppleID (or whichever ID you chose to use) listed as a pending developer profile. Now you simply have to click it and Trust the developer certificate, and voila!

8) After 7 days, your free trial developer profile will be revoked, and you must start again from Step (3). Don't worry; there is no limit to how many times you can make yourself a developer. It can become bothersome, but it's a small price to pay if you want to stay non-jailbroken.

Alternative:

-If that's a bit too much work, you can also go to Settings>General>Reset and then select "Reset Network Settings" to clear every known Wifi Network from your iPhone's memory.