You can win a Pokemon game using almost anything. A few people have successfully done that using no attack moves.
However, if you are not doing a weird challenge and care about your own time, then most status moves are useless. Although some status moves, like rest, toxic, recover, charm, heal bell, or light screen might make it easier to win battles, using them many times over the course of a game might take an extra hour. That time is much better used level grinding so your Pokemon can do more damage. As far as I know, there are 2 significant exceptions to this rule.
Moves that raise attack, such as swords dance, dragon dance, nasty plot, and quiver dance: Their purpose is pretty simple. Raising attack makes each move do more damage, so the Pokemon can more easily spam any attack and solo a gym battle or Elite 4 battle.
Accurate sleep moves, such as sleep powder, lovely kiss, spore, and yawn: Sleep moves often let your lower level Pokemon defeat a higher level opponent, so you can do less level grinding.