You should know that it's easier to select a backup drive for your laptop than for your desktop because the choices are much simpler. You are either going to choose a standard drive or you can pony up for a solid state drive.
Assuming you want a portable external drive you can carry with you in your notebook bag, your options are virtually all USB models with 2.5 inch or smaller hard drives inside a plastic or metal enclosure.
USB 3.0 portable drives are just starting to appear on the market. Among other benefits (see the 'Bus Power' sidebar in this article), the new USB version lets a drive read and write data as fast as it likes, as long as your notebook has a USB 3.0 port or adapter card.
In contrast, USB 2.0 caps data transfer to about 32MBps, which makes backups take much longer than necessary. USB 3.0 is backward compatible with USB 2.0 and 1.1 devices also.
For notebook backup purposes, it's hard to argue with the cost per GB (gigabyte) and overall capacity advantage of a portable hard drive over an SSD (solid state drive). Even though the latter will take a bit more abuse, you shouldn't notice much of a speed difference between the two.
External SSDs do exist, and they are certainly rugged enough for travel. On the other hand, capacities large enough for backup purposes are pretty costly. A mere 64GB in USB 2.0 trim will cost around $145 or more online; Plan on $220 or more for a USB 3.0 model that will not drastically limit its own speed.
You can get a 1TB (terabyte) portable hard drive for as little as $130 online. Compare this with an external SSD, which will max out at about 256GB for approximately $780 on the Web, and it's obvious that magnetic disk media is still the way to go for this application.
Look into the software that comes with a portable drive, expecially the backup app. If it's described as a drive imaging or disaster recovery tool, it backs up your operating system and programs in addition to your personal files. Some backup drives might even boot your laptop in an emergency, depending on your notebook