I highly recommend GnuCash. Not only do I use it for my personal and business accounting needs, I also use it in my role as the Treasurer of a Charity set up to keep our local library open. It provides proper double entry accounting and the ability to split transactions into different categories which enables me to use it very successfully to handle the special accounting requirements of grant spending.
Yeah, and the basics aren't even hard to learn/use, after the person understands the concept of double-entry. I know someone who has no particular expertise of accounting nor computing and who uses GnuCash to manage the money of an art group (receiving money from multiple entities, keeping track of expenses and paying out interpreters), and almost never needs help.