You can have SSL/TLS without certificates. This is supported in the TLS standard: the "DH_anon" cipher suites involve no certificate whatsoever. But you have to remember that such an unauthenticated TLS is inherently weak against active attackers, since they cannot prevent client or server impersonation (or both at the same time, which is called a Man-in-the-Middle attack).
Most Web browsers deactivate DH_anon cipher suites because of the inherent vulnerability to MitM. You can have the same conceptual effect with a self-signed SSL certificate, that you can produce yourself without talking to any CA. Of course, the same Web browsers will then show the "scary warnings", for pretty much the same reason.
From the EFF point of view, whose arch-enemy is the NSA, generalized DH_anon cipher suites would make sense, since Evil Spy Agencies™ are know to prefer passive eavesdropping (since it leaves no incriminating traces). Passive eavesdropping is defeated by DH_anon. However, for most other people, the biggest threat is not governmental intrusiveness, but mundane con-artists that try to separate you from your money, and these do not hesitate to run full MitM attacks, e.g. with fake WiFi access points.
The Let's Encrypt initiative aims at making certificate issuance free (as in "no money") and automated, while still maintaining a bit of effort at "verifying" that whoever obtains the certificate has some degree of control over the designated domain. From the look of it (it deserves closer inspection), this system relies on the DNS and implies that any DNS attack (e.g. DNS spoofing) might be leveraged into rogue certificate issuance, in a fully automated way, so this initiative would be a weakening of the current certificate model. On the other hand, if it convinces more people to use SSL, it contributes to a "safer World", at least from NSA-is-the-Devil point of view, where what matters is defeating passive eavesdroppers.
Anyway, without support from Microsoft and Google (i.e. inclusion of the Let's Encrypt root CA in IE and Chrome), there is no way that the initiative really turns into generalized HTTPS. Not a lot of people would activate SSL on their Web site if it means that 70% of users will get insulted and scared away by their browsers. If Microsoft and Google don't jump in the wagon (and I don't believe they will), then the Let's Encrypt system will remain a political gesture, but won't be widespread (and ultimately Mozilla will drop it if someone bothers to mount an automated DNS-based attack).
There is another completely different certificate-less mode for SSL; it is called SRP. That one is safe, but different from normal Web browsing. SRP ensures mutual client/server authentication with regards to a shared secret, and it does so in a way that protects the shared secret against offline brute force -- so it can tolerate the use of a low entropy shared secret, i.e. a password. TLS-SRP makes a lot of sense for accessing password-protected network resources, and it involves no certificate at all; and yet, it is safe against MitM and eavesdropping.
Unfortunately, Web browsers don't currently support SRP.
