Apple - Is there any way to view saved wifi passwords on the iPhone?
1) If you have a Mac connected to the same network, you can find the stored password in it's Keychain using the Keychain Access
app (link)
2) If the router is an Apple Airport based device, you may be able to log straight into it via Airport Utility (available on Mac and iOS) to see the password at source
3) If you are on iOS7, then you can use iCloud Keychain Syncing to allow the stored password on your iPad to be synced elsewhere (assuming you have a Mac too), allowing you to then read it in your Keychain as per point 1. In the screenshot shown, most of these WiFi networks are in other cities that only my iPhone has connected to:
Unfortunately, on the iPhone it is not possible to access this information. The passwords are kept on your phone in a safe place that is not accessible through any regular means on the phone. This is done for your protection, if you were to lose your iPhone and someone picked it up, the passwords that are stored on it would be up for grabs. This would lead to a lot of security problems.
I would recommend apps like 1password or the many other pieces of software out there that do the same thing to keep your passwords safe and backed up. I have way to many passwords to remember and it has been a life saver. 1Password even has the ability to back up your passwords to dropbox just in case something happens to your phone and you need to access it from somewhere else.
There are a lot of different password managing apps out there, just find the right one for you.
As gtm above me stated, there is a way to access your passwords but it is through jailbreaking. I do not recommend jailbreaking, that is something that you have to make the decision on for yourself. Jailbreaking is not for everyone.
I know this may not have been the answer you were looking for, we have all been there when we forget a password and there isn't a way to retrieve it. The easier thing you can do is just reset the password on your router and make sure to keep that password safe.
I hope this answer helps somewhat.
If you have a jailbroken iPhone, check out Wifi Passwords on Cydia.