Let's say the House of Representatives and the Senate pass a bill and it sits on the President's desk. Before the President signs the bill, can it be recalled (by the Senate or the House)?
This has never been tried to my knowledge, meaning the Supreme Court hasn't had a chance to weigh in on it. But the plain text of the Constitution suggests no, they can't do it.
Here's the relevant text of Article I, Section VII:
Every Bill which shall have passed the House of Representatives and the Senate, shall, before it become a Law, be presented to the President of the United States: If he approve he shall sign it, but if not he shall return it, with his Objections to that House in which it shall have originated, who shall enter the Objections at large on their Journal, and proceed to reconsider it. If after such Reconsideration two thirds of that House shall agree to pass the Bill, it shall be sent, together with the Objections, to the other House, by which it shall likewise be reconsidered, and if approved by two thirds of that House, it shall become a Law. But in all such Cases the Votes of both Houses shall be determined by Yeas and Nays, and the Names of the Persons voting for and against the Bill shall be entered on the Journal of each House respectively. If any Bill shall not be returned by the President within ten Days (Sundays excepted) after it shall have been presented to him, the Same shall be a Law, in like Manner as if he had signed it, unless the Congress by their Adjournment prevent its Return, in which Case it shall not be a Law.
Every Order, Resolution, or Vote to which the Concurrence of the Senate and House of Representatives may be necessary (except on a question of Adjournment) shall be presented to the President of the United States; and before the Same shall take Effect, shall be approved by him, or being disapproved by him, shall be repassed by two thirds of the Senate and House of Representatives, according to the Rules and Limitations prescribed in the Case of a Bill.
The system seems pretty clear-cut. "Every bill" that passes both houses gets presented to the president. From there the president shall sign, but "if not," he returns it. "Any bill" that is not "returned by the president" becomes law automatically, or fails if Congress is adjourned. "Every," "if not," "any," all suggests that the Framers intended to be exhaustive and to rule out any sort of deviations from the system they laid out.
Also, we often speak of the president "vetoing" bills, but the Constitution only speaks of the president "returning" bills to Congress. So while conceptually we might think of the president turning away a law and Congress taking it back as different things, that's not a distinction the Constitution makes. So a lawyer for the president would persuasively argue that Congress "recalling" a bill would not only violate the separation of powers by denying him his power to sign the bill, it would explicitly infringe upon a power given solely to the president.
Furthermore, if bills that have not been signed and have not been "returned by the President" automatically become law, couldn't Congress pass a law, recall it, and then watch it become law by default? That so upsets the constitutional order that I have to assume courts would step in and demand a constitutional amendment first.
Once a congressional chamber (House or Senate) has passed a measure, the only way to undo the measure's adoption is by a motion to reconsider. Such motion must be made on the same or succeeding legislative day . Since the process of sending a bill to the other chamber or to the President takes some time, this would typically preclude reconsidering a bill that has already left the chamber. Additionally, the standard practice in both chambers is, immediately on passing a measure, to move to reconsider it and immediately to table the reconsideration motion, "has the parliamentary effect of ending any possibility that another vote on the bill can take place" . So, in the typical case the passage of a bill is final before it ever leaves the chamber.
The Senate rules evidently contemplate the case where a bill is reconsidered after it is sent to the House of Representatives 
13.2 2. When a bill, resolution, report, amendment, order, or message, upon which a vote has been taken, shall have gone out of the possession of the Senate and been communicated to the House of Representatives, the motion to reconsider shall be accompanied by a motion to request the House to return the same; which last motion shall be acted upon immediately, and without debate, and if determined in the negative shall be a final disposition of the motion to reconsider.
I was unable to find any information on what happens if the motion to request the House return the bill passes, but the House refuses to do so (if indeed it is allowed to do so).
There is no mention of reconsidering a bill that has already been sent to the President, and the process of enrollment  would seem to take long enough that reconsideration would be out of order; however, in that same document I did come across this passage:
Both houses must adopt a concurrent resolution to recall an incorrectly enrolled bill already sent to the President, or to make changes in the text of an enrolled bill still in the possession of the Congress
There is an accompanying footnote giving some examples where this has happened. Based on the examples, it would seem that this procedure is only valid for making technical corrections, not for rescinding the passage of a bill, but I couldn't find any detail on the matter.
So, to summarize, most of the time the passage of a bill is final. There may be a way that both houses of Congress together can amend a bill that has been presented but not yet signed, but it's unclear whether that mechanism is limited to "technical corrections", or whether arbitrary changes can be made. Once a bill is signed by the President, of course, it becomes law, and another bill must be passed by both houses and signed by the President to change it.