Arduino Electronics

EEPROM - reading and writing to "permanent" storage
Ethernet - for connecting to the internet using the Arduino Ethernet Shield, Arduino Ethernet Shield 2 and Arduino Leonardo ETH
Firmata - for communicating with applications on the computer using a standard serial protocol.
GSM - for connecting to a GSM/GRPS network with the GSM shield.
LiquidCrystal - for controlling liquid crystal displays (LCDs)
SD - for reading and writing SD cards
Servo - for controlling servo motors
SPI - for communicating with devices using the Serial Peripheral Interface (SPI) Bus
SoftwareSerial - for serial communication on any digital pins. Version 1.0 and later of Arduino incorporate Mikal Hart's NewSoftSerial library as SoftwareSerial.
Stepper - for controlling stepper motors
TFT - for drawing text , images, and shapes on the Arduino TFT screen
WiFi - for connecting to the internet using the Arduino WiFi shield
Wire - Two Wire Interface (TWI/I2C) for sending and receiving data over a net of devices or sensors.

The Matrix and Sprite libraries are no longer part of the core distribution.

101 Only Libraries

CurieBLE - Interact with smartphones and tablets with Bluetooth Low Energy (BLE).
CurieIMU - Manage the on-board accelerometer and gyro.
CurieTimerOne - Allows to use Timer functions.
CurieTime - Allows to control and use the internal RTC (Real Time Clock)

Due Only Libraries

Audio - Play audio files from a SD card.

Due, Zero and MKR1000 Libraries

USBHost - Communicate with USB peripherals like mice and keyboards.
Scheduler - Manage multiple non-blocking tasks.

Zero and all the SAMD21 based MKR boards libraries

AudioFrequencyMeter - Sample an audio signal and get its frequency back
AudioZero - Play audio files from a SD card
RTC - Real Time Clock to schedule events
ArduinoSound - A simple way to play and analyze audio data
I2S - To use the I2S protocol on SAMD21

WiFi 101 and MKR1000 Library

WiFi101 - library to be used only with Wifi shield 101
WiFi101OTA - Over-the-air updates on MKR1000

MKR WiFi 1010, MKR VIDOR 4000, Arduino NANO 33 IoT and Arduino UNO WiFi Rev.2

WiFi NINA - library to use the WiFi Nina module of the above boards.

Arduino Nano 33 BLE, Nano 33 BLE Sense, NANO 33 IoT, Uno WiFi Rev 2, MKR WiFi 1010.

ArduinoBLE - library to use the BLE features of the above boards.

Arduino Nano 33 IoT and UNO WiFi Rev. 2

ArduinoLSM6DS3 - library to use the LSM6DS3 6 axis IMU available on the Arduino Nano 33 IoT and the Arduino UNO WiFi Rev. 2.

Arduino Nano 33 BLE and BLE Sense

ArduinoLSM9DS1 - library to use the LSM9DS1 9 axis IMU available on the Arduino Nano 33 BLE and the Arduino Nano 33 BLE Sense.

Arduino Nano 33 BLE Sense

PDM - library to use the digital microphone MP34DT05, our library PDM can be used also with our ArduinoSound library.
ArduinoAPDS9960 - library to use the gesture sensor APDS9960; it senses gesture, color, ambience illumination and proximity.
ArduinoLPS22HB - library to use the barometer and temperature sensor LPS22; it is an ultra-compact sensor which functions as a digital output barometer.
ArduinoHTS221 - library to use the relative humidity sensor HTS221; it is an ultra-compact sensor that uses a polymer dielectric planar capacitor structure capable of detecting relative humidity variations, returned as digital output on a serial interface.

MKR Motor Carrier Only Library

MKR Motor Carrier - Library to be used with the MKR Motor Carrier

MKR FOX 1200 only Library

SigFox - library to be used only with MKRFOX1200

MKR WAN 1300 only Library

MKRWAN - library to be used only with MKR WAN 1300

MKR GSM 1400 only Library

MKRGSM - library to be used only with MKR GSM 1400

MKR NB 1500 only Library

MKRNB - library to be used only with MKR NB 1500

MKR 1000, MKR WiFi 1010, MKR GSM 1400, MKR NB 1500, MKR RS485 Shield, UNO WiFI Rev.2, Ethernet Shield only Library

Arduino Modbus - library to communicate with Modbus Protocol over RS485 and TCP with Modbus clients and servers.

MKR GPS Shield Library

ArduinoMKRGPS - library to be used with the Arduino MKR GPS Shield

MKR RGB Shield Libraries

ArduinoMKRRGB - library to be used with the Arduino MKR RGB Shield
ArduinoGraphics - library with graphic primitives, works also with the MKR RGB Shield

MKR 485 Shield Libraries

ArduinoRS485 - library that implements RS485 on the Arduino MKR RS485 shield

MKR ENV Shield Library

ArduinoMKRENV - library to read all the values measued by the Arduino MKR ENV Shield sensors

MKR THERM Shield Library

ArduinoMKRTHERM - library to read the sensors connected to the Arduino MKR THERM Shield

Esplora Only Library

Esplora - this library enable you to easily access to various sensors and actuators mounted on the Esplora board.

Arduino Robot Library

Robot - this library enables easy access to the functions of the Arduino Robot.

Yún devices Library

Bridge Library - Enables communication between the Linux processor and the microcontroller on the Yún.
Ciao Library - Aims to simplify interaction between microcontroller and Linino OS allowing a variety of connections with most common protocols