The simplest depth gage is one you probably already have in your possession: the dial caliper. The depth rod, which protrudes from the end of the calipers, as you open them up, is used to measure depths with a resolution of .001" and an accuracy of .001", at least for the first 4 inches of travel. Expect an accuracy of .0015" from 4 to 6 inches. Obviously you can measure depths equal to the extended length of your calipers.
The maximum width of the depth rod is .145" on Brown & Sharpe, Tesa and Etalon 6" calipers. This dimension may limit its use, but the rod could be filed or ground to a specific profile, as long as it does not affect the length of the rod.
If you need to measure the depth of small holes you may be interested in the Shop-Cal which has a thin cylindrical rod of .060" diameter for measuring depth.
For best stability when measuring, attach a depth base to the end of the calipers. These simply slide on and are clamped in place with a screw. Before tightening the screw, place the caliper on a flat surface to make sure the depth base is flush with the end of the caliper. Some calipers come with the depth base. In other cases you may need to buy it separately.
The base allows you to firmly position your calipers over the opening in order to get a perpendicular entry into the hole. This is absolutely necessary for an accurate reading.
Because the thickness of the caliper beam varies from manufacturer to manufacturer, depth bases may not always be interchangeable between makes. The depth base shown on this page is designed for use with Swiss B&S, Tesa and Etalon dial calipers.