Some commentary over at Languagehat got me to pondering about English modal verbs. As with anything to do with language, things are a lot more complicated than you first imagine. First off, what are modals? As Steve explained, they are a class of verbs in English that are grammatically different from the other verbs. How so? Well, they don't take an -s in the 3rd person singular present indicative; no present participles in -ing; no infinitival form with to. Huh? Verbs like fear or loathe, have those forms: e.g., to fear is the infinitive, he fears is the pres. ind. 3PS, and fearing is pr. part. Modal auxiliaries, e.g., can, must, shall, don't. You can't say *he shalls.
Interesting, in and of itself, but if we take a peek back in history to Old English (AKA Anglo-Saxon) it gets even more so. It turns out that most of the modal auxiliaries developed from a class of verbs that are known as preterit-present (AKA preteritive present) verbs in Indo-European linguistics. These verbs — there are twelve in Old English — though they have forms that are in the past tense (the preterit) have present meanings. Take one of the OE verbs that became a Present Day English modal, can. In OE, its infinitive form was cunnan 'to know'. You could say ic can 'I know', hé can 'he knows', wé cunnon 'we know'. These preterit-present verbs formed their past tense in the same way as the strong verbs. Strong verbs are sometimes called ablauting verbs because different grammatical forms have different vowels, e.g., sing, sang, sung in PDE.
So, now for the second interesting bit about preterit-present verbs in OE: because they were preterit in form, but present in meaning, they developed a preterit form that was along the lines of the weak verbs. Weak verbs in English mark different forms by suffixation rather than ablaut (i.e., vowel gradation): e.g., to loathe, he loathes, he loathed. So, the past tense of can is could. You'll have to take my word that these developed from an analagous, weak past tense form, even though the vowel has change in the 1000 years or so since OE.
Here's a table of the OE preterit-present verbs (infinite), their meanings, 1/3PS form, past form, PDE present and past forms.
| ágan | possess | ág | áhte | owe | ought |
| cunnan | know | can | cúðe | can | could |
| dugan | avail | déah | dohte | dow | |
| durran | dare | dear | dorste | dare | durst |
| magan | may, be able | mæg | meahte | may | might |
| mótan | may | mót | móste | mote | must |
| munan | be mindful of | man | munde | mun | |
| (be-, ge-)nugan | suffice | neah | nohte | ||
| sculan | shall | sceal | sceolde | shall | should |
| ðurfan | need | ðearf | ðorfte | ||
| unnan | grant | an | úðe | ||
| witan | know | wat | wi(e)ste | wit | wot |
Cf. genugan with German genüg 'enough'. Another PDE modal verb is will (cf. shall) which was not one of the original OE preterit-present verbs. Owe and wit are regular verbs in PDE. Dow, mote, and mun are archaic or dialectal according to the OED.