Kant has a number of antinomies in his works -- cases where, according to him, reason naturally tends to conclude both sides of a contradiction. There really isn't any standard list, so I thought I would put together one. I've stayed with things that Kant explicitly calls antinomies. I have also given a brief indication of Kant's solution to the antinomy, although, of course, it needs to be understood that there are nuances, especially with some of the later antinomies, that the indication does not capture. Let me know if you know any that I missed.
From the Critique of Pure Reason and the Prolegomena to Any Future Metaphysics
Mathematical Antinomies (thesis and antithesis are both false)
(1) The world has a beginning in time, and is also limited as regards space. /// The world has no beginning, and no limits in space; it is infinite as regards both time and space. [CPR]
The world has, as to time and space, a beginning (limit). /// The world is, as to time and space, infinite.[PFM]
(2) Every composite substance in the world is made up of simple parts, and nothing anywhere exists save the simple or what is composed of the simple. /// No composite thing i nt he world is made up of simple parts, and there nowhere exists in the world anything simple. [CPR]
Everything in the world is constituted out of the simple. /// There is nothing simple, but everything is composite. [PFM]
Dynamical Antinomies (thesis and antithesis are true in different ways)
(3) Causality in accordance with laws of nature is nto the only causality fromw hich the appearances of the world can one and all be derived. To explain these appearances it is necessary to assume that there is also another causality, that of freedom. /// There is no freedom; everything in the world takes place solely in accordance with laws of nature. [CPR]
There are in the world causes through freedom. /// There is no freedom, but all is nature. [PFM]
(4) There belongs to the world, either as its part or as its cause, a being that is absolutely necessary. /// An absolutely necessary being nowhere exists in the world, nor does it exist outside the world as its cause. [CPR]
In the series of world-causes, there is a necessary being. /// There is nothing necessary in the world, but in this series all is contingent. [PFM]
From the Critique of Practical Reason
Virtue-Happiness Relation (thesis and antithesis are false in different ways)
The endeavor after happiness produces a ground for a virtuous disposition. /// A virtuous disposition necessarily produces happiness. [CPrR]
From the Critique of Judgment
Aesthetical/Taste (thesis and antithesis are true in different ways)
The judgment of taste is not based upon concepts; for otherwise it would admit of controversy (would be determinable by proofs). /// The judgment of taste is based on concepts; for otherwise, despite its diversity, we could not quarrel about it (we could not claim for our judgment the necessary assent of others).
Teleological (thesis and antithesis are true in different ways)
All production of material things is possible according to merely mechanical laws. /// Some production of material things is not possible according to merely mechanical laws.
From Religion within the Bounds of Reason Alone
Faith (thesis and antithesis are true in different ways)
Good works must precede faith in divine atonement. /// Faith in a merit not one's own, reconciling one to God, must precede every effort to good works.
From the Metaphysics of Morals
Possession (thesis and antithesis are true in different ways)
It is possible to have something external as mine even though I do not have possession of it. /// It is not possible to ahve something external as mine if I do not have possession of it.
Duties to self (thesis and antithesis are true in different ways; it's unclear, however, whether this is supposed to be a real antinomy or a merely apparent one)
I am the one who is obligated. /// I am the one who obligates.