His proposed amendments were:

1. Would assign seats in the House based on a scale of the size of the House: the bigger the House becomes (as the population being represented grows), the more people would be represented in each district, to try and maintain a workable-sized body. Our Constitution doesn't specify anything like this and allows Congress to determine the size of the House and the number of people represented in each District.
2. Would become the 27th amendment.
3. Protects freedom of religion and conscience; prohibits establishment of national religion. Our Constitution does not explicitly protect conscience, which is why laws like RFRA were created.
4. Freedom of speech, press, assembly, and petititon.
5. Right to bear arms. Also protects conscience objectors.
6. Protection from having soldiers quartered in private homes. Becomes 3rd amendment.
7. Becomes 4th amendment.
8. Protection from double jeopardy and self-incrimination; right to due process; protection from government seizure of property
9. Speedy and public trial and other protections for the accused
10. Trial by jury, indictment by grand jury, and other procedural and jurisdictional protections in trials.
11. Small-claims issues cannot be appealed to the Supreme Court, and "findings of fact" (things which the law says must be determined by a jury) cannot be appealed - only the legal and procedural questions decided by a judge can be appealed.
12. Right to trial by jury in civil cases.
13. Would become the 8th amendment.
14. Prohibits the states from violating freedoms of speech, religion, and press and the right to a trial by jury. These rights are incorporated under the 14th amendment.
15. Would become 9th amendment.
16. Specifies that each branch of government cannot perform the duties of the other branches.
17. Would become the 10th amendment.

So the only ones that we lost forever were his Congressional apportionment scheme and the prohibition on inter-branch crossing (which would be horrible and impractical in the modern world, where Congress cannot be expected to make every little regulatory determination). The rest were either combined to form the Bill of Rights, became later amendments, or are now unnecessary because of legal decisions under the 14th amendment.

Madison actually proposed 19 or 20 Amendments (depending on how you count some of the clauses it could be 19 or 20). Congress condensed Madison's proposals and made some significant edits, eventually passing 12 of them.

The two amendments proposed by Madison that were not passed by Congress are the following:

No State shall infringe the right of trial by Jury in criminal cases, nor the rights of conscience, nor the freedom of speech, or of the press

and

The powers delegated by the Constitution to the government of the United States, shall be exercised as therein appropriated, so that the Legislative shall never exercise the powers vested in the Executive or Judicial; nor the Executive the powers vested in the Legislative or Judicial; nor the Judicial the powers vested in the Legislative or Executive.

There were two additional amendments that made up the original Bill of Rights are these:

After the first enumeration required by the first article of the Constitution, there shall be one Representative for every thirty thousand, until the number shall amount to one hundred, after which the proportion shall be so regulated by Congress, that there shall be not less than one hundred Representatives, nor less than one Representative for every forty thousand persons, until the number of Representatives shall amount to two hundred; after which the proportion shall be so regulated by Congress, that there shall not be less than two hundred Representatives, nor more than one Representative for every fifty thousand persons

and

No law, varying the compensation for the services of the Senators and Representatives, shall take effect, until an election of Representatives shall have intervened.

This Amendment was eventually ratified in 1992 and became the 27th Amendment*

Here is the text of the original proposal that Madison made. I've noted which ones were passed and which ones were folded into other Amendments. Several of them were heavily edited, and Roger Sherman proposed that these amendments be added to the end of the Constitution, rather than be inserted into the text as Madison had originally planned (and which is normal procedure for amending bills in Congress).

First. That there be prefixed to the constitution a declaration that all power is originally vested in, and consequently derived from the people.

That government is instituted, and ought to be exercised for the benefit of the people; which consists in the enjoyment of life and liberty, with the right of acquiring and using property, and generally of pursuing and obtaining happiness and safety.

That the people have an indubitable, unalienable, and indefeasible right to reform or change their government, whenever it be found adverse or inadequate to the purposes of its institution.

This one was not passed.

Secondly. That in article 1st, section 2, clause 3, these words be struck out, to wit:

"The number of Representatives shall not exceed one for every thirty thousand, but each State shall have at least one Representative, and until such enumeration shall be made;" and in place thereof be inserted these words, to wit: "After the first actual enumeration, there shall be one Representative for every thirty thousand, until the number amounts to—, after which the proportion shall be so regulated by Congress, that the number shall never be less than—, nor more than—, but each State shall, after the first enumeration, have at least two Representatives; and prior thereto."

This one was passed by Congress but wasn't ratified.

Thirdly. That in article 2nd, section 6, clause 1, there be added to the end of the first sentence, these words, to wit, "But no law varying the compensation last ascertained shall operate before the next ensuing election of representatives."

This was passed by Congress. It was not ratified with the other Amendments in the Bill of Rights, but it ended up being ratified in 1992.

Fourthly. That in article 2nd, section 9, between clauses 3 and 4, be inserted these clauses, to wit,

The civil rights of none shall be abridged on account of religious belief or worship, nor shall any national religion be established, nor shall the full and equal rights of conscience by in any manner, or on any pretext infringed.

The people shall not be deprived or abridged of their right to speak, to write, or to publish their sentiments; and the freedom of the press, as one of the great bulwarks of liberty, shall be inviolable. The people shall not be restrained from peaceably assembling and consulting for their common good, nor from applying to the legislature by petitions, or remonstrances for redress of their grievances.

These two clauses became the First Amendment.

The right of the people to keep and bear arms shall not be infringed; a well armed, and well regulated militia being the best security of a free country: but no person religiously scrupulous of bearing arms, shall be compelled to render military service in person.

This became the Second Amendment.

No soldier shall in time of peace be quartered in any house without the consent of the owner; nor at any time, but in a manner warranted by law.

This became the Third Amendment

No person shall be subject, except in cases of impeachment, to more than one punishment, or one trial for the same office; nor shall be compelled to be a witness against himself; nor be deprived of life, liberty, or property without due process of law; nor be obliged to relinquish his property, where it may be necessary for public use, without a just compensation.

This became the Fifth Amendment

Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted.

This became the Eighth Amendment

The rights of the people to be secured in their persons, their houses, their papers, and their other property from all unreasonable searches and seizures, shall not be violated by warrants issued without probable cause, supported by oath or affirmation, or not particularly describing the places to be searched, or the persons or things to be seized.

This became the Fourth Amendment

In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, to be informed of the cause and nature of the accusation, to be confronted with his accusers, and the witnesses against him; to have a compulsory process for obtaining witnesses in his favor; and to have the assistance of counsel for his defense.

This became the Sixth Amendment

The exceptions here or elsewhere in the constitution, made in favor of particular rights, shall not be so construed as to diminish the just importance of other rights retained by the people; or as to enlarge the powers delegated by the constitution; but either as actual limitations of such powers, or as inserted merely for greater caution.

This became the Ninth Amendment

Fifthly. That in article 2nd, section 10, between clauses 1 and 2, be inserted this clause, to wit: No state shall violate the equal rights of conscience, or the freedom of the press, or the trial by jury in criminal cases

This was not passed.

Sixthly. That article 3rd, section 2, be annexed to the end of clause 2nd, these words to wit:

but no appeal to such court shall be allowed where the value in controversy shall not amount to — dollars: nor shall any fact triable by jury, according to the course of common law, be otherwise re—examinable than may consist with the principles of common law.

This became the Seventh Amendment

Seventhly. That in article 3rd, section 2, the third clause be struck out, and in its place be inserted the classes following, to wit:

The trial of all crimes (except in cases of impeachments, and cases arising in the land or naval forces, or the militia when on actual service in time of war or public danger) shall be by an impartial jury of freeholders of the vicinage, with the requisite of unanimity for conviction, of the right of challenge, and other accustomed requisites; and in all crimes punishable with loss of life or member, presentment or indictment by a grand jury shall be an essential preliminary, provided that in cases of crimes committed within any county which may be in possession of an enemy, or in which a general insurrection may prevail, the trial may by law be authorized in some other county of the same State, as near as may be to the seat of the offence.

In cases of crimes committed not within any county, the trial may by law be in such county as the laws shall have prescribed. In suits at common law, between man and man, the trial by jury, as one of the best securities to the rights of the people, ought to remain inviolate.

Parts of these two clauses were made part of the Seventh Amendment.

Eighthly. That immediately after article 6th, be inserted, as article 7th, the clauses following, to wit:

The powers delegated by this constitution, are appropriated to the departments to which they are respectively distributed: so that the legislative department shall never exercise the powers vested in the executive or judicial; nor the executive exercise the powers vested in the legislative or judicial; nor the judicial exercise the powers vested in the legislative or executive departments. The powers not delegated by this constitution, nor prohibited by it to the states, are reserved to the States respectively.

This was not passed.