Pipe Dope is not a phrase that seems to be used as much in the UK as in the US, where it seems to be a generic term for any product that is applied to threads in a liquid state. This is unhelpfully vague, as others have pointed out.
There are many different products that are applied in the liquid- (or paste-) state. Some remain liquid permanently, others set over time.
I tend to use anaerobic pipe seal on pretty much anything I intend to be permanent, with the precise product being dependent on the pressure and the perceived permanence required.
Back in the mid-1980s, I spent several months chasing down leaks on industrial hydraulics. The "best" fix for leaking threads, whether tapered or parallel, was to depressurise the system, back out the thread about half-way, give it a good dousing with brake cleaner (the system was usually still warm, so it evaporated off quickly. We used brake cleaner because it was a fraction of the price of the Loctite-branded stuff), apply plenty of Loctite 542, tighten the thread, wait a while, restart and check the leak was no more.
The Loctite method was the most boring and effective one. It avoided all the excitement associated with draining down hundreds of gallons of hydraulic oil, all the excitement of avidly watching things through the next few pressure cycles and hitting the e-stop if things got spurty, and about 90% of the cleanup associated with any of the other methods.
When I started playing with pneumatics, rather than hydraulics, I tended to stick with what I knew worked. Loctite 542 worked well, but was a bit too "strong" for threads in mixed metals that included brass and Aluminium. 577 worked well, but was much easier to undo. Then every supplier and his dog came up with their own brand of anaerobic seal, often in different strengths/grades. I find all of them work very well. They are easy to apply, don't leak and, if chosen appropriately, allow disassembly. It can be a minor pain to clean the threads for reassembly.