In general you should never have multiple display math environments (like \[ ... \] or \begin{equation} .. \end{equation}) after each other. The amsmath package provides several environments for multi-line displayed math. In this case, you want the gather environment I think.
After the first and the second matrix I added a linebreak with \\. After the third and the fourth, I added some horizontal space with \qquad.
Note also that you should have \mathbf{I}=.., not \textbf{I=}. With the latter you get the wrong spacing around the =.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{gather}
\mathbf{I}=\begin{pmatrix}
1&0&0&0 \\
0&1&0&0 \\
0&0&1&0 \\
0&0&0&1
\end{pmatrix}
\\
\mathbf{I}=\begin{bmatrix}
1&0&0&0 \\
0&1&0&0 \\
0&0&1&0 \\
0&0&0&1
\end{bmatrix}
\\
\mathbf{I}=\begin{Bmatrix}
1&0&0&0 \\
0&1&0&0 \\
0&0&1&0 \\
0&0&0&1
\end{Bmatrix},
\qquad
\mathbf{I}=\begin{vmatrix}
1&0&0&0 \\
0&1&0&0 \\
0&0&1&0 \\
0&0&0&1
\end{vmatrix},
\qquad
\mathbf{I}=\begin{Vmatrix}
1&0&0&0 \\
0&1&0&0 \\
0&0&1&0 \\
0&0&0&1
\end{Vmatrix}
\end{gather}
\end{document}
Another possibility might be using align instead of gather, and add a & before selected =, to align those horizontally.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
\mathbf{I}&=\begin{pmatrix}
1&0&0&0 \\
0&1&0&0 \\
0&0&1&0 \\
0&0&0&1
\end{pmatrix}
\\
\mathbf{I}&=\begin{bmatrix}
1&0&0&0 \\
0&1&0&0 \\
0&0&1&0 \\
0&0&0&1
\end{bmatrix}
\\
\mathbf{I}=\begin{Bmatrix}
1&0&0&0 \\
0&1&0&0 \\
0&0&1&0 \\
0&0&0&1
\end{Bmatrix},
\qquad
\mathbf{I}&=\begin{vmatrix}
1&0&0&0 \\
0&1&0&0 \\
0&0&1&0 \\
0&0&0&1
\end{vmatrix},
\qquad
\mathbf{I}=\begin{Vmatrix}
1&0&0&0 \\
0&1&0&0 \\
0&0&1&0 \\
0&0&0&1
\end{Vmatrix}
\end{align}
\end{document}
[ \textbf{I=}\begin{bmatrix} 1&0&0&0 \ 0&1&0&0 \ 0&0&1&0 \ 0&0&0&1 \end{bmatrix} ]
[ \textbf{I=}\begin{Bmatrix} 1&0&0&0 \ 0&1&0&0 \ 0&0&1&0 \ 0&0&0&1 \end{Bmatrix} ]
[ \textbf{I=}\begin{vmatrix} 1&0&0&0 \ 0&1&0&0 \ 0&0&1&0 \ 0&0&0&1 \end{vmatrix} ]
[ \textbf{I=}\begin{Vmatrix} 1&0&0&0 \ 0&1&0&0 \ 0&0&1&0 \ 0&0&0&1 \end{Vmatrix} ]
– Georgio3 Dec 18 '16 at 20:59