Pluggable Cable for multiple analog connections
In my experience, the 25-Pin DSUB cable works very well for this type of purpose. As you can tell from the name, it has 25 pins; 13 on the top side, and 12 on the bottom side, although for this purpose, cable orientation doesn't matter. The cable and female connectors are easy to come by and sell at a reasonable price. The female connectors are very simple to use, with all 25 pins sticking out the back (for ease of access, sometimes the bottom pins will protrude more than the top) and will most likely be panel-mount.

Here's an image of the DSUB and its layout: