According to Matt Cutts and John Mueller in a variety of hangouts/videos:
1. Try to get links removed only if you have a manual penalty. Otherwise, use the disavow tool.
2. The disavow tool is intended to be used only for links you've built yourself/had built on your behalf.
3. If you have links you don't like the look of, which weren't built by you, feel free to disavow them if you like, but this isn't the purpose of the tool.