Could anyone please tell me how to render passes straight to disk? I’m trying to render a Combined pass and a Diffuse Color pass, and output both to disk as the animation renders. Every tutorial I find tells how to view the passes in the Composting window, but not how to save to disk. Thank you for your help!
I think this is possible when using EXR or MultilayerEXR as output filetype, but I never used it:

Compositor add node File Output and connect to Render Layers.
It’s the Multilayer version @MelodyJane should use to get both passes in a single file. The other will just save a single image/single pass.
@MelodyJane this is the method to use if you want to save each pass into its own file.
Both answers are excellent and I learn so much every time I come here. Right now, Okidoki’s answer is what i was looking for. Thanks, Okidoki, I’m used to working with PNG sequences in separate folders and this solution gives me the kind of flexibility I’m used to. But I’m going to learn about using Open EXR, as well, LordoftheFleas, and I really appreciate this information! Thank you both for your help! 
Thank you, EAW! For now, I’m just used to having all my passes output to separate folders to import as separate footage into After Effects, so I’m liking the File Output Node method. But I’m definitely going to learn about using Open EXR with AE, and see what that advantages are. This is really good information!
Use “MultiLayer OpenEXR,” which will accomplish both objectives at once:
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All of the named layers of information will be saved into a single file, and will appear as outputs of the File Input node which refers to it.
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“The exact floating-point data streams that are produced by the rendering process for each layer” will be saved – one file per frame. (Use a separate directory/folder for each.)
This file format was designed by Industrial Light & Magic expressly for this purpose: to be an intermediate staging data file in a multi-step rendering process. (Legend has it that The Blender Foundation first came up with the “multi-layer” idea, which was promptly adopted into the standard.)
Your “final print” can be a non-multilayer OpenEXR file (directory …), since at that point you don’t need layers anymore. You then use this “pristine master” to separately generate all of the “deliverables” that your project may require – which is the first and only time that things like “compression, gamma, color grading” and so forth enter the picture, according to the needs of each delivery target.
Thank you for explaining all that, sundialsvc4! I’ll start using that format going forward. 
Note that After Effects requires a bit of set up for you to use OpenEXR files and see the same thing you see on your screen in Blender.
Checkout the video posted in this thread to explain how to do it.
Bear in mind that OpenEXR contains: “data, just data.”
When you “look at” such a file in Blender, Blender makes certain decisions about what to show you on the screen. After Effects and other software might make different decisions.
In a data file, a pixel might be “whiter tha white” or “blacker than black.” Its “color” is simply a 3-tuple of numbers that is not constrained to the range [0…1]. This is by design. One of the final steps in creating a deliverable file for a particular target is to map the data in the file to the desired visual result on that target, according to its capabilities.