Best choice between using \\ or leaving space after each paragraph to end the paragraph
there is absolutely no advantage to using \\ to end a paragraph, and in fact, a big disadvantage -- it doesn't actually end the paragraph; it only goes to a new line, and probably triggers an underfull line report in the log.
there are only two ways to end a paragraph in "basic" text mode: a blank line, or \par. there are some (but few, and mostly obscure) situations in which \par shouldn't be used. but it definitely puts something "visible" in the file, and if you are sending a file using a mailer that swallows or "disappears" blank lines, then \par is safer.
never try to end a paragraph with \\!
It's quite strange that every beginner's guide to LaTeX tells as soon as possible that
paragraphs should be separated from each other by a blank line
but several people use \\ to finish up a paragraph.
It's possible that the influence of word processors governs the choice of those who use \\. The path seems to be like
If I hit Return in the editor window for a LaTeX file, I don't get a new paragraph
In word processors, a single operation (hitting Return) does the job
Since
\\seems to make TeX go to a new line, let me use\\
This is wrong, as already pointed out. But why does TeX impose hitting Return twice, in order to end a paragraph?
There are good reasons for this, that I'll try to explain.
A (La)TeX file is pure text; text reflow and formatting takes place at a different stage than typing in the copy. Line endings and spaces are completely irrelevant because this eases maintenance of the document: we don't need to worry whether we add spaces or end lines in an irregular fashion. Editors will reflow the text, if this is wanted, but it's completely optional.
A blank line in the TeX file is a very clear marker of paragraph separation. Much clearer than the simple line ending and possible following indent in a word processor (which, I suspect, is the cause for many word processor documents that use vertical space between paragraphs). A TeX file is never to be considered an approximation of the output: it's just the container for our text, whose final form will be obtained by running (La)TeX over it.
Another reason is history. We shouldn't forget that word processors did not exist when TeX was being developed: its first release was in 1978. All one had at that time was essentially the same as the TeX model: a text file was postprocessed in order to get the final output. There were typewriters able to justify text: one had to input a line and then spaces in the line were adjusted to get justification. Another asynchronous system, which was later improved by using a buffer that could hold more copy than fitted a line and moving the excess to a new one.
Essentially the same model of these typewriters was introduced by word processors, with the advantage that text reflow was easier: the entire document could be entirely held in the buffer.
In the computing world, however, text files were the vast majority and the convention of separating paragraphs with a blank line predated TeX by several years. For pure text files, where line endings are not significant and simply mark separation between words, a blank line between paragraphs was the only feasible device.
TeXnical note. A blank line is the same as typing \par. So there is a single operation for ending a paragraph.
However, hitting Return twice is just two keystrokes and \par requires four. Moreover, the input file loses in clarity and ease of maintenance. If you want to merge two paragraphs into one, you just need to remove the blank line between them.
By the way, the same system is used on this site: paragraphs are ended with a blank line. One can type in two spaces and then hit Return
getting a new line, like here. Not the best markup, in my opinion.