Why might a machine-dependent language be more appropriate for writing certain types of programs? What types of programs would be appropriate?
The best example I can think of is for small embedded devices. When you have to have full control over every detail of optimization due to extremely limited computing power (only a few kilobytes of RAM, for example), you might want to drop down to the assembler level yourself to make everything work perfectly in those small confines.
On the other hand, compilers have gotten sophisticated enough these days where you really don't need to drop below C for most situations, including embedded devices and microcontrollers. The situations are pretty rare when this is necessary.
Why might a machine-dependent language be more appropriate for writing certain types of programs?
Speed
Some machines have special instructions sets (Like MMX or SSE on x86, for example) that allows to 'exploit' the architecture in ways that compilers may or may not utilize best (or not utilize at all). If speed is critical (such as video games or data-crunching programs), then you'd want to utilize the best out of the architecture you're on.
Where Portability is Useless
When coding a program for a specific device (take the iPhone or the Nintendo DS as examples), portability is the least of your concerns. This code will most likely never go to another platform as it's specifically designed for that architecture/hardware combination.
Developer Ignorance and/or Market Demand
Computer video games are prime example - Windows is the dominating computer game OS, so why target others? It will let the developers focus on known variables for speed/size/ease-of-use. Some developers are ignorant - they learn to code only on one platform (Such as .NET) and 'forget' that others platforms exist because they don't know about them. They seem to take an approach similar to "It works on my machine, why should I bother porting it to a bizarre combination that I will never use?"
No other choice.
I will take the iPhone again as it is a very good example. While you can program to it in C or C++, you cannot access any of the UI widgets that are linked against the Objective-C runtime. You have no other choice but to code in Objective-C if you want to access any of those widgets.
What types of programs would be appropriate?
Embedded systems
All of the above apply - When you're coding for an embedded system, you want to take advantage of the full potential of the hardware you're working on. Be it memory management (Such as the CP15 on ARM9) or even obscure hardware that is only attached to the target device (servo motors, special sensors etc).
Consider virtually any graphics engine. Since your run-of-the-mill general purpose CPU cannot perform operations in parallel, you would have a bare minimum of one cycle per pixel to be modified.
However, since modern GPUs can operate on many pixels (or other piece of data) all at the same time, the same operation can be finished much more quickly. GPUs are very well-suited for embarrassingly parallel problems.
Granted, we have high-level-language APIs to control our video cards nowadays, but as you get "closer to the metal", the raw language used to control a GPU is a different animal from the language to control a general purpose CPU, due to the vast difference in architectures.