How to safely and conventiently have an external drive connected to an OS X laptop We all know that notification 'Drive X was not ejected properly'. I have a laptop, which I use regularly at my desk with monitor etc, as well as on the go. I want to be able to back up my data to an external drive, so I've got a 1 TB drive connected via a USB hub alongside my mouse an keyboard.

It's a real pain trying to remember to eject the disk before I unplug the laptop to take it somewhere. Especially when I'm in a hurry I often forget. I've seen that notification countless times when pulling out thumb drives but nothing ever happened so I stopped taking it seriously.

That is, until my backup drive got corrupted. It's now in a state where disk utility consistently fails to reformat it and time machine can't write to it. I have two other USB devices this has happened on, but they were fairly old ones I used infrequently so I assumed something else had made them fail.

Why does OS X require users to be so careful ejecting drives? Both Windows and Ubuntu (the other two OS's I've used) seem to handle this fine. Is there a way that I can have this drive consistently connected so that backups happen automatically, but that I don't have to worry about the drive being damaged?
Actually, the assumption behind your question is incorrect. 

While other operating systems may manage the ejection of external drives differently (to some degree), they still require users to eject or safely remove them prior to physically unplugging them while the computer is still powered up.

The reason why this is important is that any computer (regardless of OS) can initiate a read or write sequence while it's powered up. It's important to note that not all read/write sequences are initiated by the user. Often they're initiated by the OS or other software, so even though you may think it's safe to remove that drive, it in fact may not be.

In terms of how you may be able to have this drive consistently connected so that backups happen automatically without the worry of damaging your drive, there's no 100% safe way without either ejecting the drive or fully shutting down a computer first. However, your next best bet is to ensure you close the lid of your MacBook prior to unplugging the laptop and taking it somewhere. By doing this and waiting a few moments the MacBook will go to sleep and unplugging the external drive will be safer (although not 100% safe).