Updated August 2016
We've all seen those questions in online forums and groups on Facebook. "Should I use Lightroom or Photoshop?". Well to tell you the truth, you want Both. Seriously... That's the answer. Lightroom and Photoshop are actually two different programs–similar yes–but different. They are designed to work together.
Adobe Lightroom = RAW Processor & File Organiser (Database).
Adobe Photoshop = Photo Editor.
I'm not going to go in depth with workflows and such, I've already got an article about that right here. Lightroom is where you will do all your rating, culling, raw processing, categorising and sorting your images. Then you'd send the image off to Photoshop to start your editing (retouching, cropping, heavy colour adjustments etc.).
There is an alternative to Lightroom however, and that's Adobe Bridge. Bridge is more complicated and isn't a RAW processor like Lightroom. Adobe Bridge is a File Management program much like Finder (Mac) or File Explorer (Windows) only much, much more powerful. The RAW processing portion of Bridge happens in Adobe Camera Raw (ACR) which is Photoshop's RAW Processor. This is like a mini Photoshop designed specifically to process your RAW files. Lightroom uses ACR too, but it's built in to Lightroom's interface rather than a separate app window.
All in all you don't want to get Photoshop or Lightroom by themselves, you want to purchase both. I recommend subscribing to the Adobe Creative Cloud. For $10 a month you get Photoshop, Lightroom and Bridge. Free updates and upgrades forever. It's the best value for money to date. To learn a bit more about Creative Cloud, I have an article below for you to check out.