Doible entry system is useful and reliable when you mainatain system for large business. If you have 100s of vendors and need to track balance between these vendors, then double entry system helps you to keep your account in check. The basic rule of having sum of different amounts in a transaction should be zero is simple and powerful in resolving conflicts.
It's also useful in the smallest of businesses. It allows for a more mature thinking about your finances and how to leverage them beyond cash=profit. It's very difficult to scale beyond a micro entity with single entry bookkeeping, for example you cannot produce a balance sheet with single entry.
