I carry all the back-up stuff in my bag - watch, depth, plastic tables. However, if I was on a multiple day, multiple dives-per-day trip and the computer failed in the middle of it, well, there goes the diving for 24 hours til I can clear out the N2 and start over with the tables.
I did lose my computer on a trip once - here is how it went:
Day 3, dive #14 - here I am, at 85 feet, la la la... Looking at the computer I have 12 minutes NDL left... blank screen! What the!.... oh, now its back on. Still at 11 minutes. Must have been a trick of the light.
Dive #15 - halfway through dive, computer blanks out again. Comes back and is still functioning (I compared with my buddy).
Dive #16 - complete failure during ascent. The computer never came back. Luckily this was the last dive of the trip so I didn't miss a thing! However, goodbye, SUUNTO...
ps - every dive was made with same buddy and we had stayed together, so we knew his computer was okay too for my profiles.