When looking at the best online backup service for Mac, there are several options with unique characteristics. There are also local backup options and hybrid solutions. All of these range in price, complexity, and will appeal to different breeds of computer users.
Best Mac backup solution: local storage or online backup?
Mac backups will either be stored locally on a hard drive(s) or with an online backup service. Online backup services have some advantages: some operate automatically when connected to the internet and files can be accessed from other devices (including smartphones). However, the automatic services typically require a monthly fee.
Local storage can be less expensive and some people may feel more comfortable not having their data backed up online (even if it is encrypted). Local storage is also at risk of and damage due to flood/fire/etc. Local storage also typically carries less redundancy, so you're at a higher risk of losing your data if a drive fails. Online backups solutions also carry these risks, but the better solutions have data stored in multiple physical locations to guard against this.
Time Machine: a free local solution
Macs come with Time Machine backup software preinstalled. Time Machine works with an external hard drive or AirPort device to backup Macs either automatically or manually. The software is simple to use, and I recommend all Mac users run it, even if you also have an online backup service. External hard drives are so affordable nowadays, there's no reason not to keep at least a few local backups of your Mac just in case.
The downside is that if you use an external drive it must be plugged in for backups to run, and there is no 'out-of-the-box' way to access your backed up files online or from a Windows PC.
Best online backup services: peace of mind has a price
There are several online backup services that will automatically backup your Mac files when connected to the internet. This ease of use and peace of mind will cost you though, as most of these services cost around $5 per month for a single computer.
There is a bit of variation between the offerings. For example, Backblaze is a simple solution with fast unlimited backup of a single computer, but it won't backup system files, and will delete backed up files 30 days after they are deleted from your computer. Crashplan will back up files forever and has options to backup to local storage or a friend's computer in addition to Crashplan's servers. If you have any special requirements search around or check out these articles from The Wirecutter and Computerworld.
What about Dropbox and Google Drive?
There are several other online storage solutions such as Dropbox and Google Drive that can be used to back up your files. These services don't offer automatic backups, but do offer a simple way to manually backup files and access them from all of your devices or share with others. They also don't limit you to uploading from a single computer. They also have mobile apps to backup photos, videos, and other files from smartphones and tablets. Both services offer free storage with more available to purchase.
My solution: a combo of local and free online backup
I use a combination of services to backup all of my files for free with a level of redundancy that I'm comfortable with. I use Time Machine to occasionally back up my Mac to a local hard drive. I also use several free apps to backup my media and documents: photos on Flickr, documents on Google Drive, and music on Google. If something were to go wrong with both my MacBook's hard drive and my external drive I would still have my most important documents backed up online and accessible from my smartphone or laptop.