Action steps:
1. If you are running Electrum, shut it down right this second.
2. Upgrade to 3.0.5 (making sure to verify the PGP signature).
You don't necessarily need to rush to upgrade. In fact, in cases like this it can be prudent to wait a while just to make sure that everything is settled. The important thing is to not use the old versions. If you have an old version sitting somewhere not being used, then it is harmless as long as you do not forget to upgrade it before using it again later.
If at any point in the past you:
- Had Electrum open with no wallet passphrase set; and,
- Had a webpage open
Then it is possible that your wallet is already compromised. Particularly paranoid people might want to send all of the BTC in their old Electrum wallet to a newly-generated Electrum wallet. (Though probably if someone has your wallet, then they already would've stolen all of the BTC in it...)
This was just fixed hours ago. The Electrum developer (ThomasV on the forum, ecdsa on github) will presumably post more detailed info and instructions in the near future.
Update 1: If you had no wallet password set, then theft is trivial. If you had a somewhat-decent wallet password set, then it seems that an attacker could "only" get address/transaction info from your wallet and change your Electrum settings, the latter of which seems to me to have a high chance of being exploitable further. So if you had a wallet password set, you can reduce your panic by a few notches, but you should still treat this very seriously.
Update 2: Version 3.0.5 was just released, which further protects the component of Electrum which was previously vulnerable.
Update 3: You definitely should upgrade from 3.0.4 to 3.0.5, since 3.0.4 may still be vulnerable to some attacks.
Update 4: Here is the official, more complete response from the Electrum dev team.
Update 5: Apparently only a minority of Electrum users have upgraded, so I'll make the news item red again for a while. No significant facts have changed since yesterday, though.