Let's say I have two separate cubes in the same scene. I want to adjust the mesh of one cube without risking unintentional alterations to the other. In 3dsmax, I remember there being a freeze modifier that kept an object visible, but you couldn't select any of it's vertices, edges, or faces. I'm looking for something similar to it in Blender.
In Blender, you don't need such a feature (not for preventing the edition of other objects, anyway) since Blender works in a different way. As I understand it, in 3DS Max you can select any vertex from any object at any time (unless, of course you freeze it, as you mention); however, in Blender, the procedure is to select an object and then go into Edit mode (Tab) on that object, which prevents you from editing other objects until you go back to Object mode (again, Tab).
As in this case it seems you created the second "object" while in Edit mode (which makes it a mesh, not an object), you can mouse over it and press L to it (actually, connected vertices) and P to make it into it's own object.
In Edit Mode you can select the vertices of the mesh you don't want to edit, press CtrlL to select all of the connected vertices, and press H to hide the vertices you want to protect from editing. AltH unhides. But not only vertices can be hidden. If you can select it, you can hide it. so this applies to a single vertex in a mesh to an entire mesh, vertex groups, and even groups of meshes in the same object. You can also use hide sequentially, so you can hide one group of vertices, do some work, then hide another group, and repeat as needed. Be aware, though, that in the present implementation, pressing the unhide key combination unhides everything that has been hidden.
In object mode, one can hide objects and groups of objects, too.
In Outline view there is an "eye/arrow/camera" row of buttons after each item is listed. The "arrow" button makes it (im)possible to select that item in the viewport, meaning you can't select it by mistake. I assume you mean you don't want to pick the wrong thing when you have several objects close together?