Just so that I'm clear; since Roundcube is open source, I'm free to use any of it's code in my own applications/projects? If this is not true, what are my options?
It depends how you want to use the RoundCube code in your project, if you where to give some information on how you plan to use and release RoundCube your projects I could be more specific. RoundCube is licensed under GPLv3 with some exclusions (full license: http://roundcube.net/license) but keep in mind that some library's that RoundCube uses are licensed differently.
Well, I'm still in the very early planning stages of this project, but I think it could borrow the code/component that is RC's backend mail client and database controller. I hope that makes sense - my terminology may be off
How are you planing to release your application?
I hope to eventually profit from the project, so I guess it'll be released commercially/closed source...?
If you use GPL libraries, your project must be released under GPL license.
As alec says if you use GPL libraries you'd have to release your project under the GPL or a GPL compatible license. Now thats not to say you can't profit from your project, there are many ways to profit from open source projects.
Okay. So I can legally use GPL libraries as long as I include it's GPL license with the conditions & terms/TOS when users sign up for my app/service?
Is your application something users will download and install on there own servers or is it a service, i.e they signup on your site and get access to an email account using RoundCube, etc.
A service. And it won't necessarily have RC's UI, mainly the backend code would be used. Essentially I don't feel like writing code that's readily available.
If its a service and your not giving any type of code or binary to anyone then you can use GPL librarys in your project.
Thanks for helping clear this up!