Can I just tap land for the sake of tapping it? Like, can i just tap a mountain for the sake of tapping it? or does it have to be for a cost?

Yeah you can tap your lands for shits whenever you want.
back in the day, you used to get mana burn, where you'd take one damage for each unspent mana in your mana pool, but they took that out to make the game more newbie friendly.

a popular example:

player one is attacking with 2 creatures
player two only has one blocker, with a contested war zone untapped on his field, so in response to taking damage, player two can tap the contested war zone so player one doesnt have an extra mana.

Tl;Dr: yes you can tap your lands for shits and giggles.