Always!
Not that that's a terrifically useful opinion to a beginner, but the fact is, you can't simply ignore many things -- maybe you'll get away with it, but they tend to have unpleasant ways of reminding you.

But you can also mitigate them. In the case of MOSFET gate capacitance, it can oscillate with connecting wires (the MOSFET itself is an amplifier with quite reasonable gain under certain conditions), and this can usually be avoided by placing a small resistor directly in series with the gate pin. Typical value is dictated by the driving source, which might be 33 to 1k ohms for a micro pin, or down to 1 ohm or even less for a power switching circuit. (Sometimes a direct connection can be used, or other components like ferrite beads or diodes; you probably won't need to know how to choose these cases, just mentioning them for information.)
If you're just switching slow, boring stuff, you should ensure that you are, in fact, switching it as slowly as you should be!
Only use as much bandwidth as you need. MOSFETs perform quite well these days: even with a 1k gate resistor to really slow it down, you can still expect sub-1µs rise times on the drain. Into a capacitive load, this can draw large surge currents; into an inductive load, this can develop large (flyback) voltages. And it doesn't take much of either to kill a transistor, and it only takes one pulse to do it.
So to cover these cases, you may think about simple, crude ways to control the environment around the transistor -- you can limit surge current by placing series resistance around it (with the load, or transistor drain or source), or using a current limiting circuit; you can limit peak voltage by placing a TVS diode from source to drain. (Pick the diode for the maximum nominal voltage applied to the terminal, then pick the transistor for the maximum peak voltage across the diode, typically 1.3-1.5 times its rating. So, a 12V supply might pick a 15 or 18V TVS, and a 30V transistor. Anything higher is fine, of course!)
This covers slow stuff; if you need faster stuff, then you should ensure that it's fast enough, but not too fast -- that's an invitation for generating radio interference. Consider applying a filter -- sometimes this can be as simple as a single capacitor or ferrite bead, or a combination with resistance (lone C's can resonate with unlucky strays or wiring; an R+C can prevent that). Typical example, digital logic signals. There are good reasons why standards exist for these sorts of things -- for example, RS232 is a slow, fairly wide voltage, single-ended standard, while RS485 is modest voltage, good current, fairly fast, and differential. Both are easy to use and well behaved.

Just wiring logic gates or MCU pins to wires -- not so well behaved, use with caution!
Tim