Solution 1:

A context strokeStyle can be a gradient:

// create a gradient

gradient = ctx.createLinearGradient(xStart, yStart, xEnd, yEnd);
gradient.addColorStop(0.0,"blue");
gradient.addColorStop(1.0,"purple");


// stroke using that gradient

ctx.strokeStyle = gradient;

Example code and a Demo using a gradient strokeStyle: http://jsfiddle.net/m1erickson/w46ps/

enter image description here

<!doctype html>
<html>
<head>
<link rel="stylesheet" type="text/css" media="all" href="css/reset.css" /> <!-- reset css -->
<script type="text/javascript" src="http://code.jquery.com/jquery.min.js"></script>
<style>
    body{ background-color: ivory; }
    #canvas{border:1px solid red;}
</style>
<script>
$(function(){

    var canvas=document.getElementById("canvas");
    var ctx=canvas.getContext("2d");

    function drawMultiRadiantCircle(xc, yc, r, radientColors) {
        var partLength = (2 * Math.PI) / radientColors.length;
        var start = 0;
        var gradient = null;
        var startColor = null,
            endColor = null;

        for (var i = 0; i < radientColors.length; i++) {
            startColor = radientColors[i];
            endColor = radientColors[(i + 1) % radientColors.length];

            // x start / end of the next arc to draw
            var xStart = xc + Math.cos(start) * r;
            var xEnd = xc + Math.cos(start + partLength) * r;
            // y start / end of the next arc to draw
            var yStart = yc + Math.sin(start) * r;
            var yEnd = yc + Math.sin(start + partLength) * r;

            ctx.beginPath();

            gradient = ctx.createLinearGradient(xStart, yStart, xEnd, yEnd);
            gradient.addColorStop(0, startColor);
            gradient.addColorStop(1.0, endColor);

            ctx.strokeStyle = gradient;
            ctx.arc(xc, yc, r, start, start + partLength);
            ctx.lineWidth = 30;
            ctx.stroke();
            ctx.closePath();

            start += partLength;
        }
    }

    var someColors = [];
    someColors.push('#0F0');
    someColors.push('#0FF');
    someColors.push('#F00');
    someColors.push('#FF0');
    someColors.push('#F0F');

    drawMultiRadiantCircle(150, 150, 120, someColors);

}); // end $(function(){});
</script>
</head>
<body>
    <canvas id="canvas" width=300 height=300></canvas>
</body>
</html>

Solution 2:

Update April 2021

Someone created an npm package called create-conical-gradient which achieves exactly the same image, but much faster.

It adds a .createConicalGradient() method to CanvasRenderingContext2D.prototype. Its syntax is:

/**
 * @param ox The x-axis coordinate of the origin of the gradient pattern, which 
 *           default value is `0`.
 * @param oy The y-axis coordinate of the origin of the gradient pattern, which 
 *           default value is `0`.
 * @param startAngle The angle at which the arc starts in radians measured from 
 *                   the positive x-axis, which default value is `0`.
 * @param endAngle The angle at which the arc ends in radians measured from the 
 *                 positive x-axis, which default value is `2 * Math.PI`.
 * @param anticlockwise An optional `Boolean`. If `true`, draws the gradient 
 *                      counter-clockwise between the start and end angles. 
 *                      The default is `false` (clockwise).
 */
const gradient = ctx.createConicalGradient(ox, oy, startAngle, endAngle, anticlockwise);

Example

const canvas = document.getElementById('my-canvas');
const ctx = canvas.getContext('2d');
const gradient = ctx.createConicalGradient(240, 135, -Math.PI, Math.PI);

gradient.addColorStop(0, '#f00');
gradient.addColorStop(0.2, '#00f');
gradient.addColorStop(0.4, '#0ff');
gradient.addColorStop(0.6, '#f0f');
gradient.addColorStop(0.8, '#ff0');
gradient.addColorStop(1, '#f00');

let isStroke = false;
const draw = () => {
  ctx.clearRect(0, 0, canvas.width, canvas.height);
  ctx.beginPath();
  ctx.arc(canvas.width / 2, canvas.height / 2, canvas.height / 2.5, 0, 2 * Math.PI);
  
  if (isStroke) {
    ctx.strokeStyle = gradient.pattern;
    ctx.lineWidth = 10;
    ctx.stroke();
  } else {
    ctx.fillStyle = gradient.pattern;
    ctx.fill();
  }
  
  ctx.closePath();
  isStroke = !isStroke;
};

draw();
canvas.addEventListener('click', draw);
<script src="https://unpkg.com/create-conical-gradient@latest/umd/create-conical-gradient.min.js"></script>
<canvas id="my-canvas" width="480" height="270">
  Your browser does not support canvas...
</canvas>

Original Answer

In my case, I needed the whole circle to be filled rather than just a stroke around the circumference. Using the answer above and setting the line width to twice the radius gave undesirable results, so I wrote my own.

/**
 * @description Options used when calling CanvasRenderingContext2D.strokeArcGradient() and 
 *              CanvasRenderingContext2D.fillArcGradient().
 * @property {Boolean} useDegrees Whether the specified angles should be interpreted as degrees rather than radians. 
 *                                (default: false)
 * @property {Number} resolutionFactor The number of lines to render per pixel along the arc.  A higher number produces 
 *                                     a cleaner gradient, but has worse performance for large radii.  Must be greater 
 *                                     than 0. (default: 8)
 */
class ArcGradientOptions {
    constructor(options) {
        function validateParam(test, errorMessage, fatal = false) {
            if (!test) {
                if (fatal) {
                    throw new Error(errorMessage);
                } else {
                    console.assert(false, errorMessage);
                }
            }
        }

        options = Object.assign({
            useDegrees: false,
            resolutionFactor: 8,
        }, options);

        validateParam(
            (options.resolutionFactor instanceof Number | typeof options.resolutionFactor === 'number') && 
                options.resolutionFactor > 0, 
            `ArcGradientOptions.resolutionFactor must be a Number greater than 0.  Given: ${options.resolutionFactor}`, 
            true);

        Object.assign(this, options);
    }
};

(function () {
    /**
     * @description Strokes an arc using a linear gradient.
     * @param {number} x The x-component of origin of the arc.
     * @param {number} y The y-component of the origin of the arc.
     * @param {number} radius The radius of the arc.
     * @param {number} startAngle Where in the circle to begin the stroke.
     * @param {number} endAngle Where in the circle to end the stroke.
     * @param {ArcGradientOptions} options Additional options.
     */
    CanvasRenderingContext2D.prototype.strokeArcGradient = function (x, y, radius, startAngle, endAngle, colorStops, 
            options) {
        options = new ArcGradientOptions(options);
        let lineWidth = this.lineWidth;
        this.fillArcGradient(x, y, startAngle, endAngle, colorStops, radius + lineWidth / 2, radius - lineWidth / 2, 
            options);
    }

    /**
     * @description Fills a sector or a portion of a ring with a linear gradient.
     * @param {number} x The x-component of origin of the arc
     * @param {number} y The y-component of the origin of the arc
     * @param {number} startAngle Where in the circle to begin the fill.
     * @param {number} endAngle Where in the circle to end the fill.
     * @param {number} outerRadius The radius of the arc.
     * @param {number} innerRadius The radius of the arc that won't be filled.  An innerRadius = 0 will fill the whole 
     *                             arc. (default: 0)
     * @param {ArcGradientOptions} options Additional options.
     */
    CanvasRenderingContext2D.prototype.fillArcGradient = function (x, y, startAngle, endAngle, colorStops, outerRadius, 
            innerRadius = 0, options) {
        options = new ArcGradientOptions(options);

        let oldLineWidth = this.lineWidth,
            oldStrokeStyle = this.strokeStyle;

        if (options.useDegrees) {
            startAngle = startAngle * Math.PI / 180;
            endAngle = endAngle * Math.PI / 180;
        }

        let deltaArcAngle = endAngle - startAngle;
            gradientWidth = Math.floor(outerRadius * Math.abs(deltaArcAngle) * options.resolutionFactor),
            gData = generateGradientImgData(gradientWidth, colorStops).data;

        this.lineWidth = Math.min(4 / options.resolutionFactor, 1);

        for (let i = 0; i < gradientWidth; i++) {
            let gradi = i * 4,
                theta = startAngle + deltaArcAngle * i / gradientWidth;

            this.strokeStyle = `rgba(${gData[gradi]}, ${gData[gradi + 1]}, ${gData[gradi + 2]}, ${gData[gradi + 3]})`;

            this.beginPath();
            this.moveTo(x + Math.cos(theta) * innerRadius, y + Math.sin(theta) * innerRadius);
            this.lineTo(x + Math.cos(theta) * outerRadius, y + Math.sin(theta) * outerRadius);
            this.stroke();
            this.closePath();
        }

        this.lineWidth = oldLineWidth;
        this.strokeStyle = oldStrokeStyle;
    }

    function generateGradientImgData(width, colorStops) {
        let canvas = document.createElement('canvas');
        canvas.setAttribute('width', width);
        canvas.setAttribute('height', 1);
        let ctx = canvas.getContext('2d'),
            gradient = ctx.createLinearGradient(0, 0, width, 0);
        
        for (let i = 0; i < colorStops.length; i++) {
            gradient.addColorStop(colorStops[i].offset, colorStops[i].color);
        }
        
        ctx.fillStyle = gradient;
        ctx.fillRect(0, 0, width, 1);
        return ctx.getImageData(0, 0, width, 1);
    }
})();

This method draws lines from the center of the circle to each pixel along the edge of it. You get a cleaner gradient this way.

Circles side-by-side

For large line thicknesses, it's still cleaner.

Rings side-by-side

Its one major drawback is performance. If your radius is very large, the number of lines required to produce a nice circle is about 50 times the radius.

jsFiddle

Solution 3:

I needed this effect, too a few days ago, and I have managed to create a workaround to achieve it.

What I did was overlay one gradient over the other using something like this:

var ic = [
      /*0*/{ a:"#FEC331" ,b:"#FB1E24"     ,r1:0   ,r2:1   ,x0:0   ,y0:rd*0.5 ,x1:0  ,y1:-rd},
      /*1*/{ a:"#FEC331" ,b:"#FB1E24"     ,r1:0.5 ,r2:0.5 ,x0:0   ,y0:rd*0.3 ,x1:0  ,y1:-rd},
      /*2*/{ a:"#EA6F2B" ,b:"transparent" ,r1:0   ,r2:1   ,x0:-rd ,y0:0      ,x1:rd ,y1:0  }
  ];

Here's the complete code and demo in JSFiddle:

https://jsfiddle.net/flamedenise/n9no9Lgw/33/

Hope it helps.