Sending data from Arduino to the server where arduino (sketch) acts as a client
A simple HC-05 module will give you a wireless bluetooth connection.  They're fairly simple to setup, and you can write data to them the same as one would the Arduino serial console.  Obviously they can read data too.

SoftwareSerial bt_serial(2, 3); // RX | TX
bt_serial.begin(9600);

[...]

if (led_state != last_led_state)
{
    if (led_state == HIGH)
        bt_serial.print("1");
    else
        bt_serial.print("0");
    last_led_state = led_state;
}


On the "server" side, a simple program reading the mapped bluetooth serial port would do the job.  For example, some python code:

import serial
import sys

serial_port = serial.Serial(port='COM8:', baudrate=9600, bytesize=serial.EIGHTBITS, parity=serial.PARITY_NONE, stopbits=serial.STOPBITS_ONE)

try:
    serial_port.open()
except:
    print("Failed to open port")
    sys.exit(2)

while (True):
    try:
        led_state = serial_port.read()
        if (led_state != 0):
            print("LED is on")
        else:
            print("LED is off")
    except:
        pass

serial_port.close()   # yes, it never gets here