Are auxiliary verbs as strange in other languages as they are in English?

In English, auxiliary verbs like should, would, could and ought have no conjugated forms. Can has the conjugated form could Other than for can, to form past tense you use have as in I should have gone. There is no distinction between present and future tenses. You can’t use will with an auxiliary.

In high school Spanish class, the only auxiliary verbs I remember are poder and deber, roughly translated as can and ought. Checking online, I see they can be conjugated like any other Spanish verb.