Automatic Paragraph Numbers (\everypar only for paragraphs and not for \section and so on)

One approach using the linguex package:

\documentclass{article}
\usepackage{lipsum} % for dummy text    
\usepackage{linguex}
% Counter format 
\renewcommand{\ExLBr}{\bfseries}
\renewcommand{\ExRBr}{}
% http://tex.stackexchange.com/a/57279/11604
% Reset \ex. at each section 
\usepackage{chngcntr}
\counterwithin{ExNo}{section}
% add section counter
\renewcommand{\Exarabic}{\thesection.\arabic} 
\begin{document}
\section{First section}
\ex. \lipsum[2]\par
\ex. \lipsum[3]\par
\section{Second section}
\ex. \lipsum[3]\par
\end{document}

Edit: If yo do not want any command starting the paragraphs, use \everypar at your own risk ... you are warned in the comments.

In the next MWE, the macro \NumPar at the beginning of each section produce the same output that above. As example of the problems about using \everypar, note that a new section cancel the numeration but do not restore the default indentation of 1em, so you must restore it manually.

\documentclass{article}
\usepackage{lipsum}
\parindent1em
\begin{document}
\def\NumPar{%
\parskip0.5em%
\parindent0em%
\everypar={%
\hangindent3em%
\addtocounter{subsection}{1}%
\makebox[3em][l]{\bfseries\thesubsection}%
}}%
\section{First section}
\NumPar
\lipsum[2]\par
\lipsum[3]\par
\everypar{}
\lipsum[3]\par
\section{Second section}
\NumPar % Or \parindent1em to return to normal paragraphs
\lipsum[3]\par
\lipsum[3]\par
\end{document}