amps and speakers

It depends.  "3-way" or "4-way" (or 2-way) speakers always contain internal crossovers for the high frequency drivers, or in higher-end models include external crossovers.  These should always be used (except in very specialized and advanced installations.)  But since most small cone woofers (like most 5.25 or 6.5 inch speakers) cannot produce much bass, so it can be a very smart thing to add a high-pass crossover to protect them from the low frequencies they can't produce anyway.

Also, a subwoofer ALWAYS needs a low-pass crossover of some type regardless of the other speakers in the system.  It is common to use an external crossover for this, and many of them will include a high-pass output for the main speakers.