I'm rebinding melee and skill power activation to keys closer to the WASD keys to make them more accessible. I was going to rebind Q, but by default it is set to "Secondary Use".
The only use of that key in-game that I've noticed so far is that it allows you to shop with NPCs instead of just talking to them. Are there any other uses for this key?

2 Answers
Secondary use button is used when you can chose between multiple interactions with an NPC;like with Marcus and Dr.Zed where you can either use "E" to simply talk to them or use "Q" to enter their shop interface.
Another example is when you finish a certain quest for Claptrap and you can press "Q" to ask him for a high-five.
As you and @dave-mcclelland mentioned, Secondary Use is used for:
- for NPCs and items that have multiple types of interactions: opening the store (like Marcus for example), giving Claptrap a high-five, turning off radios, etc.
- dropping items**
** Though right now it appears to be a bug (I assume) that even though Secondary Use can be remapped on the PC, dropping items stays with the hard-coded Q key — according to @Brysonic. I tested this in my PC copy too.
4