Overall as a breed, Malinois comes to mind. Siege makes Trent look like a stubborn rock and Trent's a German Shepherd.
"Easiest to train" really depends though, because in theory, sure...but in reality I really have to find the right balance with Siege when it comes to training/rewards. She's hard to physical corrections but fairly handler soft, and many rewards are overstimulating to the point where she simply can't think because she just wants that reward SO **** BAD.
Trent tends to be more deliberate and think things through and realize what I'm asking of him, though in the end, Siege picks up on things a lot quicker because she'll offer behaviors continuously and is much more driven for her reward.
I think any herding breed in a general sense, but things vary so much between dogs, you could take pretty much any breed bred besides the hound and guardian breeds and could probably easily find a biddable, handler oriented dog. and even in those types you can find those dogs, but i think generally speaking, obviously the dogs bred to work "with" people not just "for" them will have more of those traits
Oh, I should add that in NO way do I find GSDs lacking in biddability, and have known plenty of German Shepherds more biddable than some Malinois. Depends on the dog, depends on the training, depends on how they're raised, etc.
A large part of Trent's relative lack of biddability is how I raised him (incorrectly), but also his uncharacteristically independent nature, and handler hardness.
Like RTH said, there can be a huge spectrum in any breed.
IMO it depends on what you're asking of the dog and how to fill their needs and wants. Any dog can be brilliant in their own way.
Border collies are pretty easy to train, and are very biddable - unless they decide you're not worth listening to or think you're mistaken.
Papillons are pretty easy to train, and are very biddable if they love you. They are little tyrants if you let them run the show.
Labradors are very easy to train by the book which is pretty much any book but have a harder time with the more abstract concepts that papillons bridge to much more easily and quickly. They love food, and mostly like you - especially if you have food or a fetch item but I don't find my lab especially motivated by just my desires alone like most of my papillons are.
Some of the problem might be that breeds bred to be super biddable are also bred to work. A lot. A dog who is always energized and ready to work with and for you might have a hard time living the easy pet life at home.
Cynder is VERY biddable. She will do what you tell her to do, when you tell her to do it. She hates water and hates swimming, but once swam out to sea because Michael had waded out and called for her. But trainable? Pfffft. I can't even teach her to sit reliably on command because she's so soft she shuts down when any pressure is put on her - including following a lure.
Abrams I would also say is biddable. He tries SO HARD to do what you want. He's also very motivated and loves to work. That being said, he's not the sharpest tool in the shed, so he can't grasp tricks and things as quickly as my collie mix back home could. But, since he's not the sharpest tool in the shed, he also doesn't get in to near as much trouble as my collie mix did. LOL
Echoing what others have said above, a biddable dog is often less than easy to live with. I personally find herding breeds in general and border collies and cattledogs in particular to be wonderfully biddable. My cattledogs seem to wait with baited breath for a command so they can snap to it and then beg for another. Someone naturally chill is not going to follow you around going "Look at me! I sat! I know something! OMG tell me to do something else!"
I wrote a long post on here this morning, but lost it
Basically, the jist was that "biddable" is a pretty subjective term, and someone with less experience as a handler and trainer is going to have a different idea of a biddable dog than an average pet owner trying to teach house manners. People who participate in a ton of dog sports or working activities might be looking for the kind of biddability a malinois or border staffy has, whereas someone looking to get a CGC and teach fun tricks to a therapy dog that is primarily a family pet is going to have a really different idea.
Some of the breeds I've worked with where I've met a lot of very biddable individual dogs:
Great Swiss Mountain dogs (but I've only known a few and they may have been from the same lines)
Pit Bulls - the more "watered down" lines that are common up here, not what are considered "hot" working line dogs.
I think it's a lot easier to look at what dogs aren't biddable.
Also, in which ways do you want the dog to be biddable? Do you want the dog to be looking at you for direction regarding house manners at home, and be easy to teach simple tricks and basic manners to? Do you want a working dog? A dog that is going to be very focused on you naturally in public places/with distractions?
I think the best direction I could point someone looking for "biddable" as an average or hobby sport dog owner is that lower drive, more pet/show bred herding dogs (aussies, GSDs, BCs, even OES), or sporting breeds that aren't as super-excited about strangers/stimuli (think springers, chessies, etc. VS labs or cocker spaniels) are going to be a good start.
I could also name breeds that are generally super biddable (like some people said, malinois, working bred GSD, IME rotties, lots of sport-bred BCs, even JRTs, etc) but are going to need a lot of training and management to make that biddability usable over their really high instinct intelligence, reactive tendencies, etc.