In English, what makes a modal (morphologically) a modal is three properties: use as an auxiliary, the absence of either participle, and the simple present stem inflecting as if it were the simple past stem - that is, the third person present singular uses the bare form rather than a hypothetical -s form. With the loss of "thou" and the slow but steady death of the subjunctive, it certainly looks like the modals don't inflect at all, especially when grade schoolers are taught all nine modal stems as separate words, rather than the four and a half they actually are. And this isn't even getting into the semi-modals "need" and "dare" that @jlawler talks about.
What does the subjunctive have to do with modals? Well, the subjunctive uses the simple past stem, hence "if it were". When "will" became the future tense indicator, it's past stem became the future tense indicator of counterfactual conditionals, where the subjunctive is used.
If I give them a present, they will like me more.
If I gave them a present, they would like me more.
If I had given them a present, they would have liked me more.
See the difference? Similarly for "can/could":
If I study, I can pass.
If I studied, I could pass.
If I had studied, I could have passed.
Note how the modal absorbs the subjunctivity of the main verb - it's "could pass", not "could passed" or "can passed", and similarly with "could have".
"May/might" and "shall/should" behave the same way:
If you kiss me, I may kiss back.
If you kissed me, I might kiss back.
If you had kissed me, I might have kissed back.
(This is only an example, not an invitation.)
If the user breaks the widget, he shall fix it.
If the user broke the widget, he should fix it.
If the user had broken the widget, he should have fixed it.
The fact that "should" carries less weight than "shall" is a side effect of suppletion by "must" - which does carry the full weight.
If the user broke the widget, he must fix it.
Speaking of, "must" is the only modal about which Anderson is completely correct - the present stem has been wholly replaced by the past stem in all cases, so it truly never inflects.
And this on top of the fact that "could" still sees use as "was able to", and "should" as "was required to" - the legitimate past tenses of their respective present stems.