What's the maximum number of squadmates I can lose on a successful ME playthrough?
All of them!
Explanation and unmarked spoilers ahead:
Throughout the game, do everything you can to drop your War Score. Avoid sidequests, punch journalists, piss people off, and get everyone killed. We're going for the worst ending ever here.
Kill Wrex in ME1. I'm not sure if this is 100% necessary with the ending but it's completely unambiguous this way. Ashley or Kaiden will also die on Virmire but we'll kill the other one later.
Jenkins also dies.
Do Samara's loyalty mission. Either you kill Morinth or you recruit Morinth and kill Samara. Since they're both potential squadmates, I'm counting this as another kill.
End the suicide mission with as many people as possible dead. Ideally you want only two (the minimum for Shepard to survive) survivors. I won't go into the details as the suicide mission is complicated enough to be its own question. See below for the most easily killed choices.
Destroy the collector base so your only choice will be the Destruction ending.
In Mass Effect 3, get the remaining squadmembers from 2 killed. The ones that can be done in the main plotline are:
- Thane: Always dies
- Mordin: Cure the genophage and he dies in the process
- Jack: Ignore Grissom Academy. She will be turned into a Phantom and encountered and killed in the Cerberus base
- Tali: Wipe out the Quarians so Tali kills herself.
- Legion: Shoot him to stop him transmitting to the geth. Alternatively, don't activate legion and he's in the Cerberus base
- Miranda: Don't warn her about Kai Leng
- Morinth: Always dies; is encountered as a Banshee
- Zaeed: Dies if disloyal
The following can be killed but you need to go out of your way or do sidequests to do so:
- Samara: Let her commit suicide at the end of Lesuss
- Grunt: Save the Rachni Queen on Utukku and he'll die if he isn't loyal
Other squad members cannot be killed in ME3 so must die in the suicide mission.
During the coup, fail to talk Ashley/Kaiden down and kill them.
Finally, get the worst ending with James and Liara as your squad. Harbinger will kill them in the final push. Pick destruction, destroying all the synthetics in the galaxy to kill EDI.
ME1 - You can kill Wrex and either Ashley or Kaidan will die. That's 2 kills.
ME2 - It's easy to kill off nearly everyone in the suicide mission. As long as you don't do their loyalty mission death is a very likely outcome. You just need to make sure two squadmembers survive so Shepard survives as well. Best options for those two are squad members who will or can die in ME3, i.e. Miranda, Mordin, Thane, Morinth (Morinth and Thane WILL die in ME3 no matter what, so they are the best choices; Studoku lists a few more options and what exactly to do to kill them in ME3). That's 11 kills (13 squad members total, 2 must survive)
ME3 - Kaidan/Ashley can die during the Coup, if you fail to talk them down (Thanks @Studoku, didn't remember this could happen). You can choose to never awaken Javik. This leaves you with Liara, EDI and James, i.e. three people as the minimum number of squadmates possible. That's 4 kills (Kaidan/Ashley, Javik + the two survivors from ME2)
This leaves a total of 17 dead squadmates before the final push. For this answer I discounted everything happening after you start the final push, as this is the games ending, not the final mission. Technically EDI dies in the destroy ending and your 2 squadmates die during the final push with low warscore.