Scrum is based on empirical process control model (as opposed to defined process). It is a simple inspect and adapt framework for managing complicated and complex projects (most creative processes, e.g. software development projects, are complex and this is why Waterfall, which is a defined approach, doesn't work for them1).
In other words, Scrum is well suited for projects with a lot uncertainty, not only software development projects (note that, unlike XP, Scrum isn't prescriptive about software engineering practices and this is intentional). Actually, Scrum has been used:
- to manage a school, a library, a church
- to manage a weeding a someone pointed out
- for the creation of startups
- for marketing projects
- for Sales and Support
- etc
Regarding software to help with the process, FORGET THEM during learning/adoption phase (what the hell do people have with tools?). Don't let a tool drive your process i.e. how you should do Scrum, you want to learn Scrum, not how to use a tool. So start with the simplest thing that could possibly work: a spreadsheet and a whiteboard and post-its.
1 Applying waterfall to software development again and again and expecting it to work because, this time, you won't tolerate any change always reminds me of the following quote: "The definition of insanity is doing the same thing over and over again and expecting different results" --Albert Einstein