How to make smooth circles in Photoshop without jagged edges

I tried numerous times to make a smooth circle, but I kept ending up with jagged edges in Photoshop. I knew I had been missing something and that's what kept spoiling my design. I then realized - hey, unlike Illustrator, Photoshop isn't a Vector tool. It is a Raster tool. But there must be something I could do to get a perfect smooth circle. And this did the trick:

For circular shapes:

• Select the Ellipse Tool
• On the top panel, change the mode from Shape to Pixels. 
• Tick the Anti-alias checkbox.
• Now draw your shape!

For circular selections:

• Select the Elliptical Marquee Tool
• Tick the Anti-alias checkbox.
• Now go ahead and make that selection!

While making selection from a path:

• Make sure that the 'Anti-Aliased' checkbox is ticked.

For a better understanding of the Anti-Alias feature, see the comparison image below (Click to enlarge):