Does that stop power grabbers and statists? If only. There are some who follow this though.
The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States;
This is a big one. As I've covered previously, the so-called "Welfare Clause" is meant to restrict the powers of the federal government, not allowing them to do something unless it provides a direct benefit to everybody, not a benefit to 51% and a burden to 49%.
Congress has the power of taxation. Until 1913, they didn't have the power of income taxation, and generally resorted to ill-advised protectionist tariffs. Regardless, Congress has the power to tax for defense of the nation and to provide courts and police to defend our rights. (Yes, the police are meant to defend rights, contrary to popular opinion.)
Though this is an ill advised action, Congress still has the power to do so.
To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes;
An equally controversial statement, the so called "Commerce Clause". Some have attempted to use it to defend Obamacare. Others have attempted to use it to cripple business and industry with obscene regulations. However, I believe the purpose of this clause is clear. It was meant to give the power of "regulating Commerce" to the federal government, which in turn would restrict states from regulating commerce amongst themselves.
Now, if the federal government used that power strictly to prevent states from regulating commerce, that would all be well and good. But, as we can learn from the so called "Gilded Age" (which was actually one of the most prosperous periods in American history), if Congress has the power to abuse, they will likely abuse it.
To establish an uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;
This makes a pretty good amount of sense. Though the United States is a confederation of several states, it still exists as one nation for purposes of war, citizenship, etc. By providing uniform naturalization laws, it prevents someone losing citizenship (or naturalization) the second they cross state lines.
To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;
Keep in mind the Congress has the power to coin money. Not to delegate the power of printing (not coining) money to a semi-government central bank that abuses it by blindly printing off money whenever it feels like (The Federal Reserve). So, Congress can regulate the value of money, but it also is only granted the power to coin money. That is, to create money that is backed (or made of) solid metals with tangible value, not worthless paper and ink.
To provide for the Punishment of counterfeiting the Securities and current Coin of the United States;
Counterfeiting currency is just another way to debase currency. If you can't trust the metal content of the coins used, the value will go down. Surprise surprise, when our "coins" (Federal Reserve Notes) don't have any metal content or any tangible value, the value goes down. Who knew?
To establish Post Offices and post Roads;
This is not an authorization for the construction of massive interstate highways. This is merely an authorization for the federal government, if it chooses to do so, to create roads for the purpose of mail delivery.
To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;
Many libertarians are against this provision, but I support it. This establishes copyrights, meaning something that an individual created, designed, invented, or wrote is guaranteed to be their private property, to be used however they see fit. I see this as protection of individual rights. It's not like somebody's right to murder you takes precedence over your right to live. Likewise, your right to your own mind takes precedence over another's right to it.
To constitute Tribunals inferior to the supreme Court;
Not everything can be settled by the Supreme Court (and as we'll discover in Article III, not everything should be).
To define and punish Piracies and Felonies committed on the high Seas, and Offences against the Law of Nations;
Piracy used to be a much bigger problem in the Atlantic and Caribbean than it is today. Granted, there are still plenty of pirates, and Congress has the authority to deal with them, when it concerns American interests/American citizens.
To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water;
The Congress of the Untied States, and the Congress alone, has the authority to declare war. Not the President. Not the United Nations. The Congress, the most direct conduit to the people, has the power to declare war, which it has not done since 1942.
To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years;
This was an early attempt to restrict army raising to two years. All it really does is provide for new money appropriation to the armed forces every two years, the same length of time for a term in the House of Representatives.
To provide and maintain a Navy;
Seeing as how airplanes didn't exist yet, the Constitution originally provided for an Army and a Navy. Today, the Coast Guard and the Marines are linked to the Navy, while the Air Force is linked to the Army, though they are all their own distinct branches of the military.
To make Rules for the Government and Regulation of the land and naval Forces;
The Congress (or rather, the federal government) makes the rules for the armed forces of the federal government. This is common sense, and in no way was meant to detract from the power and freedom of militias.
To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
The militia was a decentralized group of American citizens. Rather, there were many militias, which varied from state to state. They were rarely professional soldiers. They were American citizens who were ready to defend their nation if the need arose.
To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress;
The federal government (Congress) will only be in control over the militias when they are serving to defend the United States as a whole, with no regards for what they may do within their own state. The states, meanwhile, may appoint officers, and train the militias.
To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings; — And
The Congress legislates for the new seat of the federal government, not constructed as of the writing of the Constitution. Today, we know it as Washington D.C, located between Maryland and Virginia.
Likewise, this grants the federal government authority of lands it purchases from the states for the purpose of forts, arsenals, and other such essential things required by the military. (Note, this does not allow the federal government to purchase acres upon acres of trees. Trees are not needful buildings. They are trees.)
To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.
Another "clause" the statists love to reference, the "Necessary and Proper Clause". In actuality, all this does is provide for the writing of laws not explicitly stated in the Constitution, providing that the laws are created are made only for the purpose of executing powers, such as making a post office, or declaring war.
That is literally all that the Congress of the United States is authorized to do. However, if you take one glance at Justin Amash's Facebook page (where he posts every vote on every bill in Congress), you'll find that the Congress is following no such restrictions, preferring to regulate every aspect of your life and the free market, and restrict what both are permitted to do. If only more of them bothered to read Article 1: Section 8.