line-breakingparagraphs
In certain styles of text I define \parindent 0pt in the preamble and write the text in this manner:
paragraph 1\\
paragraph 2\\
and so forth. I wonder if there is anything I can include in the preamble for instance to modify how the end of paragraphs are interpreted so I don't have to include the \\ at the end of each?
As the comments on your question said, you want one of \smallskip, \medskip, bigskip, or \vspace{<amount>}.
As an example (note that \vspace accepts absolute length in pt, mm, cm, or in, and relative length with ex—the height of an 'x' in the current font—and with the more common em, the width of an uppercase 'M').
\documentclass[12pt]{article}
\begin{document}
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
\smallskip
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
\medskip
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
\bigskip
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
\vspace{3.5mm}
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
\vspace{10mm}
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
\end{document}
produces
If a document indents the first line of a paragraph (in TeX jargon, the indentation amount is governed by the \parindent length parameter), one usually does not provide extra vertical space between ordinary paragraphs, i.e., the length of the \parskip parameter is 0pt by default.
Conversely, some - but certainly not all - document styles that set \parindent to zero also set a non-zero amount of \parskip. Otherwise, situations can easily arise where the reader wouldn't be sure if a parapraph break is present or not.
In TeX and LaTeX, a paragraph break is generated automatically whenever one or more entirely-blank lines in the input file are encountered. It is considered bad form to generate line breaks through \\ instructions (and unpleasant things can happen if you do it anyway).
Somewhat different considerations apply for "out-of-the-ordinary" paragraphs, such as theorems. There, one generally does want to generate some visual separation from the surrounding, ordinary-text paragraphs. Just how much extra vertical space is inserted above and below the theorem depends on whether you've loaded certain theorem-related packages such as ntheorem or amsthm; the latter is loaded automatically if you use a document class such as amsart.
Coming to your final question, there are indeed differences, in terms of the vertical space above display-math material, depending on whether \[ ... \], \begin{equation} ... \end{equation} or one of the amsmath multiline equation environments such as align and gather are used. For more information on this subject see, e.g., the postings abovedisplayskip vs abovedisplayshortskip and Un-indent all paragraphs and increase the space between paragraphs.
Best Answer
Use
or perhaps better use
and never end a paragraph with
\\it just makes LaTeX generate loads of warnings and poor typesetting.