You can use the titlesec package to change the way \paragraph formats the titles and set the secnumdepth counter to four to obtain numbering for the paragraphs:
\documentclass{article}
\usepackage{titlesec}
\setcounter{secnumdepth}{4}
\titleformat{\paragraph}
{\normalfont\normalsize\bfseries}{\theparagraph}{1em}{}
\titlespacing*{\paragraph}
{0pt}{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex}
\begin{document}
\section{Test Section}
test
\subsection{Test Subsection}
test
\subsubsection{Test Subsubsection}
test
\paragraph{Test Modified Paragraph}
test
\end{document}

If you want to define a new sectioning command, you can take a look at Defining custom sectioning commands.
If you want to define a fresh new sectional unit below \subsubsection, but above \paragraph, then you will have to do considerably more work: a new counter has to be created and its representation has to be appropriately defined; the sectional units \paragraph and \subparagraph will also have to be redefined, as well as they corresponding \l@... commands (controlling how the will be typeset in the ToC if the tocdepth value is increased); also, the toclevel (for eventual bookmarks) will have to be considered.
Here's an example showing how to obtain this new sectional unit giving you now the option to use \part, \section, \subsection, \subsubsection, \subsubsubsection, \paragraph, and \subparagraph:
\documentclass{article}
\usepackage{titlesec}
\usepackage{hyperref}
\titleclass{\subsubsubsection}{straight}[\subsection]
\newcounter{subsubsubsection}
\renewcommand\thesubsubsubsection{\thesubsubsection.\arabic{subsubsubsection}}
\renewcommand\theparagraph{\thesubsubsubsection.\arabic{paragraph}} % optional; useful if paragraphs are to be numbered
\titleformat{\subsubsubsection}
{\normalfont\normalsize\bfseries}{\thesubsubsubsection}{1em}{}
\titlespacing*{\subsubsubsection}
{0pt}{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex}
\makeatletter
\renewcommand\paragraph{\@startsection{paragraph}{5}{\z@}%
{3.25ex \@plus1ex \@minus.2ex}%
{-1em}%
{\normalfont\normalsize\bfseries}}
\renewcommand\subparagraph{\@startsection{subparagraph}{6}{\parindent}%
{3.25ex \@plus1ex \@minus .2ex}%
{-1em}%
{\normalfont\normalsize\bfseries}}
\def\toclevel@subsubsubsection{4}
\def\toclevel@paragraph{5}
\def\toclevel@paragraph{6}
\def\l@subsubsubsection{\@dottedtocline{4}{7em}{4em}}
\def\l@paragraph{\@dottedtocline{5}{10em}{5em}}
\def\l@subparagraph{\@dottedtocline{6}{14em}{6em}}
\makeatother
\setcounter{secnumdepth}{4}
\setcounter{tocdepth}{4}
\begin{document}
\tableofcontents
\section{Test Section}
test
\subsection{Test Subsection}
test
\subsubsection{Test Subsubsection}
test
\subsubsubsection{Test Subsubsubsection}
test
\paragraph{Test Paragraph}
test
\subparagraph{Test Subparagraph}
test
\end{document}
