Some believe that if you're main profession is pure math research, you don't need a scientific calculator. That's simply not true. Although I don't use one nearly as much as when I was an undergrad, I still need a calculator and the only one I'm willing to use is the Casio FX-991MS.
A first look reveals a typical scientific calculator. It has all the basic elementary functions like factorial, sin, cos, tan, hyperbolic versions of those, logs, powers, and roots. It also has permutations and combinations.
What makes this model stand out is its two-line input method. It displays equations as you enter them, and with the four-way pad you can move around and edit existing equations including several dozen past calculations in memory.
That already is pretty cool. But even better, you can include up to nine distinct variables in your equations. These variables are accessed via the ALPHA+KEY combination, where KEY is any key on the calculator with a red letter above it. Once a variable is included in your equation, you can press the CALC key and the calculator will ask you to input values for each of the variables appearing.
This equation substitution feature is a huge time saver for tests in subjects like physics, where you need to use the same equation many times. With the FX-991MS, you just have type it in once. Since the calculator doesn't have permanent memory, you can still use it for closed-book tests.
Another useful feature is the inclusion of 40 of the most common physical constants (like the mass of the electron or the speed of light) as well as 40 metric-imperial conversion units.
There is also an equation solver that probably uses some kind of Newton's method, and you need to input an initial guess value. For example, it took about 2.8 seconds to solve $\sin(x) + x = 1/2$. This could be surprisingly handy if you are doing some applied work like physics and you have an odd equation to which you need a quick and dirty numerical approximation.
Modern computer programs can do all of this too. But the FX-991MS gives you a compact solution to do quite a variety of calculations without needing a computer. And there are times where you might not have power for a computer, tablet, or smartphone. With this calculator, I've replaced the battery twice since 2005 and it's still going strong. In addition, it can run on solar power so a battery isn't even necessary as long as there is sufficient light. I'd also like to say that this calculator is still superior to a smartphone or computer when you need to do basic numerical calculations due to the tactile feedback of the keys.
There are a few features that I think for most people won't be very useful. There is a vector and matrix mode, where you can input up to 3×3 matrices, multiply and add them, and find their determinant. It's a hassle to even enter a matrix on a calculator like this, and it's faster to do these calculations by hand. There is a complex number mode, but it's half-baked. You can't calculate trig functions of complex numbers and you can't raise a complex number to an arbitrary power (though you can square and cube one). Instead of including complex numbers or a matrix mode, this calculator would be better off if there were additional functions like density or cumulative distribution functions of some common distributions.
The build quality of this calculator is good. Mine looks a little beat up, but it has had no problems. The Casio FX-991MS is hands down the best calculator I have used, and will sets the bar for any competitor.