If the drives date from 2006, I could see copying the data off of them – but you might not want to use them as data storage drives, or as your main backup drives, going forwards.
Hard drives that have been used a lot may be prone to failure. Those that have been sitting unused for a very long time may develop problems like the lubricant gumming up and keeping the drive from spinning up properly. (SSDs are not immune from long-term decay, either; leave them unpowered for years and the data might "evaporate".)
Also, there's been a bit of improvement in hard drives since 2006. You may find that you can consolidate the data from all four of those old hard drives onto a single modern hard drive (which you would then want to back up) – so that you only need a single-drive enclosure on your desk, instead of a possibly noisier four-drive one.