How do I make two objects pull toward each other in a zero-gravity scene? I have two spheres in a zero-gravity scene. I'd like for them to gradually float toward each other until they collide. This makes sense, since in real life everything has its own gravity.

I have removed the gravity from the scene and created two rigid body objects, with a very high mass, but they just remain static and never float toward each other.

I can add a Force Field to one with a negative value which pulls the non-force fielded sphere toward it, but if I add a force field to both spheres, they again remain motionless.

How do I set up a scene so that both spheres react to each other's gravity?
To make the your rigid bodies attract in your scene (assuming you already added your rigid bodies), you need to do this for each object:

1- Add a Force Field: In the 3d view, press ShiftA > Force Field > Force

2- Make your object the parent of the Force Field: Shift + Right click on the Force Field, followed by your object (The order is important) > Ctrl+P > Parent

3- Make sure your origin is on the center of mass of your object:
Select your object, then in the tools panel, select Set origin > Center of mass

4- Align the Force Field to your object: Click on your object > Shift+S > cursor to selected, Click on the Force Field > Shift+S > Selected to Cursor

5- Modify the settings of the Force Field: In the properties panel physics tab, you can find the settings for the force field. By deafult, the strength is set to a positive value, which will push objects apart. To make them attract, input a negative value. Note that massive/distant objects will require a lot more strength to be effective.

Repeat this process for every object in your scene, and you will have your magnetic attraction the next time you click play.