There are definitely two schools of thought on this; the purists who say you should only use a BT and tables, and the computer crowd. I'm definitely in the computer crowd. IMO, there are a lot more drawbacks to NOT using a computer than there are to using one.
If you are diving a known site, with a square profile, then tables and timers are fine. Anywhere else, there is a significant advantage to be gained by using a computer.
It is great to learn on tables, however. Kind of like learning basic mathematics when you were a kid, putting together your own tables, calculating your own gas plan, doing all of those things builds some very necessary fundamental skills that everyone should do. Once you understand the basics, just like you did in school, you buy the damn calculator.
This is not to say that tables become less important when you use a computer. Cutting your tables is still a necessary component of the dive plan; primarily for gas, CNS, and contingency planning. I'll run a plan, extended plan which varies based on the dive plan (+5min/5ft for deep dives, +10/+10 for nitrox), max gas, and bail-out (1/2 BT) plus lost gas scenarios. I'll have all of this information on my slate in case my computer buys the farm, but this also helps me understand what my gas plan and required gas for the dive.
I dive a Shearwater Pursuit, backed up by tables (usually cut on V-planner or Free Planner). Running 20/90 gradients will put out roughly the same plan as V-Planner @ +3. The shape is a little different but RT's, gas, and CNS is as close as you can get. I would use Free Planner (same algo as the Pursuit) but I hate having to convert liters into CF and it's not as user friendly as V-planner.