Infinite loops are taught as evil. Is there ever a good use?
When coding them by accident, the CPU peaks and I imagine memory does too, especially if assigning variables inside the loop.
If there is a good use, how are those issues prevented?
First of all, the word "infinite" in this phrase should be taken a bit more loosely. I am presuming you are talking about a while (true) loop with a break instruction, which will eventually end, as opposed to a loop which will run until the end of time and all humanity.
In the former sense, yes, there are use cases where it's appropriate:
Games use infinite game loops.
Embedded programs use infinite main loops.
Windows applications use infinite message loops.
One example where they might be used inappropriately is when they are used to create time delays by spinning the CPU, which is what novice programmers tend to do to avoid dealing with timer interrupts (or timer events, or other non-procedural constructs). However, when spinning the CPU is done to acquire a shared resource, then the "infinite loop" is also a perfectly valid implementation choice. Even the .NET CLR Monitor, for example, tries spinning for several hundred cycles before issuing a true wait on a kernel event handle and creating a more expensive thread switch.