Many services also offer a feature called versioning. This saves incremental changes you make to files as recoverable snapshots of the file. It's useful in case you need to get back information from an earlier version or if your latest file save becomes corrupted. Services vary widely in how many versions they keep and how long they're saved. Best-in-class services, such as SOS Online Backup and SpiderOak ONE keep an unlimited number of file versions forever.
CrashPlan is completely free if you're just doing local backups, but even online backups are affordable, with CrashPlan+ accounts starting at $2/mo (per computer) for 10GB of online backup storage, and going up to $4/mo (per computer) for unlimited online backup storage and $9/mo for unlimited online backup storage for a whole household. You can check out their plans here, and try them free for 30 days with a new account.