Left-aligned text is the standard because it gives the reader a vertical anchor to jump back to on every line. You should use it for most of your body text (unless you have a very good reason not to).
Center-aligned text doesn’t have that anchor, so it’s easier for the eye to get lost when it tries to jump to the next line. Reserve it for special kinds of content, like poems, lyrics, and headings.
Only use right-aligned text when it makes sense for the layout. For example, a caption for an image:
Of course, if you’re publishing content in a language that’s read right-to-left, that’s another story...
Justified text requires a good hyphenation engine. Without an intelligent way to split long words across lines, you get big spaces between words, which makes it harder to scan the text. Most browsers don’t have good built-in hyphenation engines.