Sorry, but I disagree with most of the posts on this topic. If you are a purely recreational diver, staying above about 90 feet, you do not need to use the tables. The computer will do an excellent job calculating the NDC time you have left at any given moment and will time a safety stop for you.
Back some years ago I refused to buy a camera with automatic exposure, believing my use of a hand-held exposure meter and setting the f-stops myself was the only way to be sure. Today, virtually all professional photographers (there are a few exceptions), the guys whose living depends on them getting the exposure right every time, use only automatic and don't give another thought to the computer in the camera that makes the necessary calculation and adjustments. Years before that, my father wouldn't buy a car with an automatic transmission... you get the point.
You do need some sort of back-up to be able to complete a dive if your computer fails while you are at depth. I wear a dive watch that includes depth, time (duh) and an ascent speed warning alarm. This will allow me to ascend safely, including the timing of a 3 minute stop at 15 feet.
Now, what happens to your subsequent dives if you computer fails and you use your dive watch to ascend is a different question. If I'm on a one day dive trip, I might take the chance my day will get shortened, as I don't think the odds are high that the computer will fail. If I'm on a liveaboard for a week, I'll strap on a second computer for every dive; if the main one fails, I can jump right back into the water on the next dive with the spare. But I'm still not using tables.
As for the comment a few posts back,
"Some carry 2 or more (computers)... but by some off-chance, all could fail at the same time as well..."
I'll live with that risk. Probably means there's been a nuclear electromagnetic pulse, in which case the simultaneous failure of all my computers and backups will be the least of my problems.