Scrum can be used at all levels, as others have pointed out, it can be done alone as a scrum of 1. Likewise, you can have "scrum of scrums" which is essentially a pyramid of scrum teams. Each team focuses on a feature or related feature sets. The teams would elect a member or two to represent that feature team to a larger audience (they don't need to meet daily!) and that group can move up ... You can also switch the representatives up, but I'd suggest doing that in between sprints, which is the best general time to make changes.
The most important thing that I say to anyone starting out with scrum is:
- Start with the basics, don't get caught up in fancy software! Use index cards, marker boards, etc. The only exception to this rule is if the team is dispersed.
- For the first several sprints, play by all of the rules of scrum. Only make drastic changes after you have several sprints under your belt. This way if the process doesn't work for you, you know that it wasn't because of an immediate change you've made.
- Keep changes out of the sprint. Management doesn't like this idea because they want control, but right up front have an agreement that product changes happen between sprints.
- find a "scrum sponsor" that is someone who has been through some sprints and can offer assistance (but not interference).
Good Luck!