Apollo abort modes
During the launch of an Apollo spacecraft by the Saturn IB or Saturn V rocket, the flight could be aborted to rescue the crew if the rocket failed catastrophically. Depending on how far the flight had progressed, they would use different procedures or modes. None of these launch abort modes was ever used on any of the fifteen crewed Apollo spacecraft flights.

Houston's announcements of the current abort mode and the spacecraft commander's acknowledgements were among the few things said on the radio link during the first minutes of flight.

If the rocket failed during the first phases of the flight, the Emergency Detection System (EDS) would automatically give the command to abort. The reason is that life-threatening situations can develop too fast for humans to discuss and react to. In the later, less violent phases of the ascent, the EDS was turned off and an abort would have to be initiated manually.

Overview

Of the five abort modes, the modes up to three (III) are variations of jettisoning the entire rocket followed by an immediate landing in the sea (splashdown). Mode four (IV) and the Saturn V-specific modes are variations of jettisoning only the failing rocket stage, using the other stages to continue into Earth orbit. Once there, a backup Earth-orbit mission could be performed so that the flight was not entirely in vain. In all cases, the Command Module (CM) with the astronauts performs a splashdown by: 
 Dumping the hypergolic fuel overboard since the toxic substance would be an unnecessary risk to recovery personnel.
 If high enough, deploying high-speed parachutes (drogue parachute).
 Jettisoning the drogues and deploying the main parachutes.
 Splashing down in the sea and waiting for recovery team to arrive.

Details
Apollo's planned-for abort modes were, in chronological order:

Pad abort: 
If the rocket failed in the last five minutes before launch, the CM and the launch escape system (LES, see figure) would separate from the remainder of the rocket below with the LES propelling itself and the CM beneath it upward and eastward to the sea using a small solid-fueled motor (the launch escape motor) at the top of the tower on the launch escape system. The launch escape tower would then be jettisoned in anticipation of the parachute deployment and the CM would splash down. (Preparation for a pad abort is seen in Apollo video footage: five minutes before launch, the umbilical arm connecting to the CM retracts and swings clear of the rocket. It does so because the swing arm must be out of the way in case the EDS decides to abort.)
Pad Abort Test-1: Launch Escape System (LES) abort test from launch pad with Apollo Boilerplate BP-6.
Pad Abort Test-2: LES pad abort test of near Block-I CM with Apollo Boilerplate B-23A.
Mode I: Abort using the LES, from launch until LES jettison 30 seconds after second stage ignition.
Mode IA (one alpha): During the first 42 seconds (Saturn V) or 60 seconds (Saturn IB) of flight – up to  – the rocket is still relatively upright and an abort is much like a pad abort. The main and pitch control motors move the CM out of the flight path of the possibly exploding rocket. Fourteen seconds into the abort, the LES tower is jettisoned, leading to splashdown.
Mode IB (one bravo): From  to 30.5 km (100,000 ft), the rocket is tilted eastwards far enough that firing the pitch control motor is unnecessary. After the LES main motor moves the CM away from the rocket, the tower would deploy canards (small wings at the tip). They would force the CM-LES combination to fly with the CM bottom forward (blunt-end forward or BEF attitude), necessary because the parachutes stowed at the CM top were only designed to be deployed in a downwind direction.
Mode IC (one charlie): From 30.5 km (100,000 ft, or about 19 miles) until the LES is jettisoned, turning the CM-LES combination around into the CM-forward position would still be necessary, but in the now thin air the canards are useless. Instead, the small engines of the CM's reaction control system (RCS) would do the job. During One-Charlie, the first staging occurs, that is the jettisoning of the spent first stage and ignition of the second stage. One-Charlie ceases about 30 seconds after the staging when the LES is jettisoned, at an altitude of about 90 km (295,000 ft or 55 miles).
Mode II: With the LES gone, the Command/Service Module (CSM) would separate as a whole from the rocket and use its large engine and RCS engines to move clear of the rocket and align itself. The CM would then separate from the SM and splash down.
Mode III: For use when a Mode II type abort would risk the spacecraft coming down over land, or landing in the cold waters of the North Atlantic. The CSM would separate from the rocket in the same manner as a Mode II abort, but would additionally use the SPS engine to make either a posigrade burn (Mode IIIA) or retrograde burn (Mode IIIB) to land in a specific area on the eastern side of the Atlantic. Mode III was only available as a primary abort mode for 10–15 seconds during a Saturn IB launch, and was only used as a backup abort mode for Saturn V launches, in case of an abort requiring the immediate landing of the spacecraft.
Mode IV: Abort during S-IVB burn. Should the S-IVB fail, the Service Module engine can place the CSM in Earth orbit to perform an Earth-orbit mission.
Mode V: Only planned for the Apollo-Soyuz Test Project launch. In the event of an early S-IVB shutdown, the CSM RCS thrusters would be used to insert the entire stack (including the docking adapter) into orbit. The time window for a Mode V abort was only 1.5 seconds before nominal S-IVB cutoff.

For Saturn V launches, two additional abort modes were available:

S-IVB to COI: ("Saturn IV-B (NASA's designation for the Saturn V's third stage burn) To Contingency Orbit Injection") In case of an S-II failure, the stage would be jettisoned, and the rocket is high and fast enough that the S-IVB stage, followed by the Service Module (SM) engine, has enough propellant to place the spacecraft in Earth orbit. There would not be enough propellant to perform trans-lunar injection, so only an Earth-orbit mission would be performed.
S-IVB to orbit: The failing S-II would again be jettisoned, but Earth orbit insertion is now possible by the S-IVB alone. Other than not using the SM engine, this is identical to an S-IVB to COI abort.

During orbital abort phases (S-IVB to COI, S-IVB to orbit and Mode IV), modes II and III were available as backup modes in the event of further problems.

The EDS was enabled for the pad abort (beginning 5 minutes prior to launch) through abort mode IB phases. Beginning in mode IC, the EDS was switched off and aborts would have had to be commanded manually.