More etymological spelling help from the Online Etymology Dictionary.

Define: c.1384, from O.Fr. definir "to end, terminate, determine," from L. definire "to limit, determine, explain," from de- "completely" + finire "to bound, limit," from finis "boundary." Definite (1553) means "defined, clear, precise, unmistakable;" definitive (c.1386) means "having the character of finality." Definition is recorded from 1645 as a term in logic; the "meaning of a word" sense is from 1551.

So "definite" and "definitely" have common roots with both "define" and "finite". Therefore it's never "definately".

Here's another.

Despair: c.1325, from O.Fr. desperer "lose hope, despair," from L. desperare "to despair," from de- "without" + sperare "to hope," from spes "hope" (see speed). Noun replaced native wanhope.

I like "wanhope" myself. It sounds pale and wistful.

Ran across the Spanish name "Esperanza", which is rendered "Hope" in English. This helps me remember that "desperate" means "without hope". "Desparate" is more like "disparate", meaning unequal (without parity).