How to list dependent packages (reverse dependencies)?

apt-cache rdepends packagename should do what you want

aptitude has a fairly nice way of handling this:

$ aptitude why bash
i   foomatic-filters PreDepends bash (>= 2.05)

By default, it only lists the "most installed, strongest, tightest, shortest" reason, but you can use aptitude -v why to make it output everything it finds.

apt-cache showpkg <pkgname> 

Example:

apt-cache showpkg lightdm

The simplest option is still:

apt rdepends package-name

which does not require you to install any package.

There is more than one way, with each method showing a different output.

For a detailed view of the full reverse dependency tree;

aptitude install apt-rdepends
apt-rdepends -r bash

Alternatively;

apt-cache showpkg bash

Or a concise list:

apt-cache rdepends bash

In addition to other good answers, an apt/apt-get -s does a "simulated" removal (or install).

sudo apt -s remove <pkgname>

Using -s or --simulate to remove (or install) packages, will normally list any dependencies affected. It will show orphaned packages when removing, or needed dependencies when installing, without actually executing the install or remove. Informational only.

With the reverse-depends command from the package: ubuntu-dev-tools

reverse-depends libjs-openlayers
# For build depends search
reverse-depends -b libjs-openlayers

Reverse-Recommends
* gis-osm

Reverse-Depends
* cyclograph
* phpmyadmin
* sumo-tools

Packages without architectures listed are reverse-dependencies in: amd64, arm64, armhf, i386, ppc64el, s390x