from The American Heritage® Dictionary of the English Language, 4th Edition
- auxiliary v. Used to express obligation or duty: You should send her a note.
- auxiliary v. Used to express probability or expectation: They should arrive at noon.
- auxiliary v. Used to express conditionality or contingency: If she should fall, then so would I.
- auxiliary v. Used to moderate the directness or bluntness of a statement: I should think he would like to go.
from Wiktionary, Creative Commons Attribution/Share-Alike License
- v. Used to form the future tense of the subjunctive mood, usually in the first person.
- v. Be obliged to; have an obligation to; ought to; indicates that the subject of the sentence has some obligation to execute the sentence predicate.
- v. Will likely (become or do something); indicates that the subject of the sentence is likely to execute the sentence predicate.
- v. A variant of would.
- n. A statement of what should be the case as opposed to what is the case.
from the GNU version of the Collaborative International Dictionary of English
- Used as an auxiliary verb, to express a conditional or contingent act or state, or as a supposition of an actual fact; also, to express moral obligation (see shall); e. g.: they should have come last week; if I should go; I should think you could go.
from The Century Dictionary and Cyclopedia
- n. Preterit of shall.
From Old English sceolde, preterite form of sculan ("owe", "be obliged"). (Wiktionary)