Safari stopped using keychain Safari 7.0.2 on OS X 10.9.2 stopped using keychain and doesn't remember passwords any more.

That's on my iMac. On my Airbook it still works.

I checked in the keychain application and some of the passwords are stored there and some aren't (but used to be). But Safari is not using any of them.

Any ideas?
You must have already checked that, but just in case, under Safari &gt; Preferences &gt; Passwords make sure that that the AutoFill user names and passwords checkbox is selected.
If it does not work and you are using iCloud Keychain :
On the official Apple Support Website, there is an article about Troubleshooting iCloud Keychain. Here is what it advise you to do :
First make sure that your device is currently on a Wi-Fi or cellular network. If the connection appears strong, try these steps:

 1. Turn off iCloud Keychain on all devices.
 2. Enable iCloud Keychain on the device that has the most up-to-date
    keychain items.
 3. Enable iCloud Keychain on your other devices. They will be updated
with your new iCloud Keychain.

When you enable back iCloud Keychain, DO NOT FORGET to do it — as explained by Apple — on the device with the most up to date version of you list of passwords (in your case it must be your MacBook Air).
Hope it helps.