For the diffuse term Lambertian is still the norm. There are definitely more complex diffuse models out there which could be feasible for use in a game (Oren-Nayar, Disney's Burley model) but the computational cost is generally not really worth it compared to a Lambertian term.

For specular lighting it seems that Cook-Torrance with a GGX normal distribution function (NDF) is becoming the norm as opposed to (Blinn-)Phong. Not sure what you could call the "norm" for the other Cook-Torrance components, but I've seen the Smith geometry term adjusted for GGX used quite frequently. The fresnel term is pretty much always Schlick's approximation.

For ambient we're sort of moving away from the flat single color ambient model in favor of proper indirect diffuse and specular lighting models (which is what ambient wanted to approximate). There's a large amount of different ways to approach indirect lighting and is a pretty complex subject.

EDIT:

Just to add, if you're just starting out there's no reason not to learn the Phong or Blinn-Phong specular models. In general these are much easier to understand and allow you to play around with relatively intuitive parameters so you can learn the in and outs of what works and what doesn't when it comes to a specular lighting model. You shouldn't worry about what "modern" games use just yet.

I have used Phong and Blinn-Phong models for quite a while. Just doubt those games nowadays use lighting model as simple as Phong Shading.

I'm sure there's still plenty of games using Phong or Blinn-Phong, it's been used to create some pretty stunning stuff in the past and is still much cheaper to use than any physically based model. If you're targeting mobile or low-performance devices you can't really afford to use expensive lighting models.

Coincidentally I've just been reading this...

http://www.frostbite.com/wp-content/uploads/2014/11/course_notes_moving_frostbite_to_pbr.pdf

It's a pretty extensive discussion of the lighting and material models used in the Frostbite Engine, from SIGGRAPH 2014. It opens with a good discussion of microfacet models and specific handling of diffuse and specular, punctual and area lights, etc.

If we're talking PBR in general these are mandatory reading material:

SIGGRAPH 2013 Course: Physically Based Shading in Theory and Practice

SIGGRAPH 2014 Course: Physically Based Shading in Theory and Practice

Especially the course notes and slides on "Physics and Math of Shading" by Naty Hoffman are pure gold.