This is pretty open ended the way its asked.  Are you developing a module from a starter kit?  Or are you installing a packaged module from a 3rd party?  What version DNN?  Without posting specific info in your question, I cant give a specific answer.  So I'll give all answers I can think of.

If installed a module from a package:
-It either failed to install and therefore wont show OR
-it is a Skin Object, which is only useable in the page markup, not in the Select a Module drop down.

If you are developing a module from a starter kit:
This would happen if there was an error running the SQL script for the module, OR if you fail to run BOTH scripts.

Example:  after creating a module called "widget" you will find these two files in your module code folder:

01.00.00.SqlDataProvider
widget.SqlDataProvider

You must copy and run the code from these as host in the SQL page, with the Script box checked, in the order I listed (one at a time).

If your modules fail to show up at this point, I can't help you without more detail.  Maybe someone else has more ideas than me that can help.

I found another possible cause of this.  A serious bug.

This assumes you are running 4.3.x, and are adding a new Module Definition from the Add New Module Definition link.

Problem:
If you add a module using the Module Definition tool, you must be CAREFUL.  Naturally, you want to scroll down to find a "submit" button at the bottom (called Update in this case).  BUT if you click that Update button you will find your module HALF installed in a screwed up state.  It will allow you to see it in the drop down but not add it to the page if you click Add!

Furthermore:
If you are in this state, you are hosed.  You cannot re-install, you cannot uninstall, you cannot fix this.  Unless you know what 3 tables to edit, you are screwed.

This is the only table that gets a record for your module:
DesktopModules

These are the other 3 tables that need related records:
ModuleDefinitions
ModuleControls
Modules

Once I added records in these tables, it seemed to fix the problem.

Conclusion: 
DO NOT click UPDATE at the bottom when adding new Module Definitions.  You must click INSTALL  (small link to the right of the drop down list of available modules to add).


Suggestions for Core team:
This should be logged (if not already) as a bug in the tracker.  I would check,  but at the time of discovery and writing this, the tracker was down.

Bug 1: 
Usability issue.  User naturally heads to bottom of page after filling out fields, and will inevitably click Update when in fact Install is what needs to be clicked.  Do not mix installing and updating module definitions into the same UI.  Thats just asking for catastrophe.

Bug 2:
For the love of all that is good and holy... Block running the Update code on a module definition that doesnt exist.  Prevent database corruption (incomplete records) from happening when trying to Update a module definition that has not even been installed/added yet!

Note:  If you fix bug 1, then bug 2 can never happen anyway.  I'm a huge advocate of good and proper UI, and there is one of many reasons why.