Remember, there are different types of Creative Commons licences. If you pick music that does not have the NonCommercial condition, you don't need to worry about whether your software is free, ad-supported or paid-for (but do remember to check what other conditions apply, such as Attribution and NoDerivs).
I'm not a lawyer, but if you're making money, either directly from sales, or indirectly from selling adverts, then I would consider that commercial.
For example, the human-readable page of the Attribution-NonCommercial licence says:
Noncommercial — You may not use this
work for commercial purposes.
The full legal code says:
You may not exercise any of the rights
granted to You in Section 3 above in
any manner that is primarily intended
for or directed toward commercial
advantage or private monetary
You'll get "private monetary compensation" from adverts.
Edit: so the added example is Attribution Noncommercial (3.0), which means you cannot just take it and use it in commercial software. However, Creative Commons licences are not exclusive:
Waiver — Any of the above conditions can be waived if you get permission from the copyright holder.
So you can still go and ask the creator (the copyright holder) directly for permission to use it how you want, and if you agree terms (free use, in return for something (money or credit)) then the CC licence no longer applies.