It originally belonged only to an inflected form of the infinitive, expressing purpose; as in the Old English, "Ūt ēode se sǣdere his sæd tō sāwenne" (Out went the sower his seed to sow).
Cases when to is omitted.
But later, when inflections became fewer, to was used before the infinitive generally, except in the following cases:—
(1) After the auxiliaries shall, will (with should and would).
(2) After the verbs may (might), can (could), must; also let, make, do (as, "I do go" etc.), see, bid (command), feel, hear, watch, please; sometimes need (as, "He need not go") and dare (to venture).
(3) After had in the idiomatic use; as, "You had better go" "He had rather walk than ride."
(4) In exclamations; as in the following examples:—
"He find pleasure in doing good!" cried Sir William.—Goldsmith.
I urge an address to his kinswoman! I approach her when in a base disguise! I do this!—Scott.
"She ask my pardon, poor woman!" cried Charles.—Macaulay.