Encrypted WiFi with no password?

Here's a crazy idea - put the password in the SSID. An SSID can be up to 32 characters long, which is plenty of space to both describe your network and communicate the password, as long as you're reasonably creative.

My Free Wifi "Password123"

For a no password setup, try WPS (http://en.wikipedia.org/wiki/Wi-Fi_Protected_Setup) This will allow your network to be encrypted with WPA(2) without the hassle of passwords or pin codes. OK, small lie - there is still a password (A requirement for WPA Encryption); However, users never need to know the password.

When used correctly WPS is a lot like pairing Bluetooth devices together. One button press will pair the computer with the wireless router.

WPS is supported by Windows XP+, Linux, and Mac. WPS is support on any router that has the Wi-Fi Alliance Certification sticker on the box (Any modern router that cost more than $20 will have this).

So basically the security is not within the key itself, but within the ability to have physical access to the router.

EDIT: Clarifying point of Max Nanasy

There are two types of WPS, Pin code security and hardware security. Max Nanasy you are referring to the pin code brute force method. I myself have cracked networks with this brute force attack. However, this method only works when the pin code ability is turned on. WPS can be used without the pin code. I have found depending on the router the WPS pin code exploit is useless. For example, all modern D-Link routers will disable WPS pin authorization (until an administrator re-enables it) after ~10 failed pin codes.

Hardware security as I talked about above requires a cracker to have access to the hardware of the router (and if a person has that, they can do anything, i.e. get your Windows passwords, house security passcodes, etc.).

To my knowledge only workarounds exist, such as giving the password away via SSID or other means, or having an empty password. That way the communication can still be secure (depending on the configuration).

You can use WPA-802.1X (often called "WPA-Enterprise") with various EAP versions, some of which (EAP-TLS, EAP-IKEv2) work using X.509 or similar asymmetric keypairs.