My website doesn't contain too sensitive data. I'm thinking about storing passwords as is because if a user wanted to receive their password by email (if they'd lost it) then I'd be able to send it to them rather than doing anything cumbersome and grueling to users like sending them a new password I created (it's also ineffective).
Should I just store them as is?
The passwords are sensitive data - people use them across sites, you don't want it to leak, or to be visible - not even to you or your programmers.
No, you should hash them. Most users have the same password on multiple sites, so even if your site is not too sensitive there could be other sites with the same username and password that are more sensitive.
If users forget their passwords, send them a new one.
No. The password might not be important from your site's perspective, but naive users tend to reuse their passwords. You might be holding, say, a user's bank account password. You should even apply a random salt that is stored with the hashed password (usually as a prefix string), so that the same password can't even be identified across sites or accounts.
The default answer is YES, HASH (AND SALT) THE PASSWORDS, in screaming caps.
The reason for this is that the majority of users use the same password for all sites that they log on to, so if your site is ever compromised, then all those passwords are out in the open.
I ran a website sometime ago and I can suggest: do not store plain text passwords. Many users use same password for several applications and, if your site is compromised, they will blame you.
Hash your passwords and send a new one, with expiration time, if your user lost it.
Atleast encrypt them and then decrypt when needed. There are quite a number of encryption techniques. Eg DES, Triple DES, TRIPLE_DES etc. Or you can create some simple technique yourself.
I am not sure in what language you are coding but most of the modern programming languages like c#, java already have libraries for encryption. You can use them also.
Why the dilemma? You should probably not be developing account management system yourself. Take some standard component of password management, and save yourself debugging and security bugs.
NEVER EVER store your password in clear in the database. And please tell what other websites you developped so I never create an account on them.
Definitely hash them, there is no reason not to. You can even encrypt the password in the user's browser and just transmit the hash, e.g. with the code used here.
use openid (http://openid.net/) and dont worry about password management.