I still use slide rules.
They take a little more strategy to solve problems than a calculator does, but they're faster than a calculator once you get the hang of them. You have to break that idea that all problems have to be in a format of (73)(45) = x before solving them. Most times, it's faster to solve your problem when the variable is buried somewhere in the middle of the equation. I know I want my answer to be 45, so I'll just scan down the scale for all the division problems that equal 45 until I get to 73 and then see what I had to divide by.
You have to buy a good graphing calculator before you reach a point where a calculator is capable of solving more types of problems, as well. I can solve problems with complex numbers, solve quadratic equations, do coordinate transformations from Cartesian to polar (or even spherical) - all things the cheaper calculators can't do. Of course, my TI-86 can solve cubic equations, or even higher powers. It can solve matrix problems, do cross products, etc, all a lot faster than you can on a slide rule. Plus, the graphing functions can make it easier to find roots for equations, area, etc than actually solving the problem.
Of course, you run into the same problems with slide rules that you do with calculators. As they get more elaborate with 20 some scales that make it quicker to solve different types of problems, you can forget the basic scales worked just as well at getting you an answer. Calculating something like the doping concentration of a semi-conductor can throw you for a momentary loop when you're working with numbers higher than your beloved log-log scales go.
You get a basic simplex slide rule with an A, B, C, D scales, a base 10 log scale, and your trig functions, Tan, Sin, and small angle Tan/Sin scale, you're really good to go for just about any problem. I still like my
N4-ES vector hyperbolic dual base speed rule with it's 34 scales.
That slide rule actually works, by the way click on the slide and move it around; click on the cursor and move it around. Mine is slightly different - mine was the initial version, so it doesn't have the copyright, and has only 33 scales (I don't have the Ln scale above the L scale). Mine is in a lot better shape with no rust, as well.
(My avatar is a close up of the pocket Pickett N600-T my dad gave me).