You need to use \addplot+[only marks]:
\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[]
\addplot+[only marks]
coordinates{(1,2)(2,3)};
\addplot+[only marks]
coordinates{(1.2,2.2)(2.2,3.2)};
\end{axis}
\end{tikzpicture}
\end{document}
The + makes \addplot use all the default options (cycling through the markers) plus the options you specify (only marks).
To further shorten that, if you want to use the option only marks on each \addplot inside a tikzpicture you can use:
\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}[only marks]
\begin{axis}[]
\addplot
coordinates{(1,2)(2,3)};
\addplot
coordinates{(1.2,2.2)(2.2,3.2)};
\end{axis}
\end{tikzpicture}
\end{document}
Alternatively you can also give this as an option to axis (\begin{axis}[only marks]).
To change the cycle list used you can use the option cycle list name=<name> in the options of axis. Predefined cycle list are listed in the corresponding section of the package documentation.
You can also provide your own cycle list:
\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}[]
\begin{axis}[only marks,
cycle list={
{blue,mark=*},
{red,mark=square*,mark options={fill=green}},
{mark=o},
{yellow,mark=+},
}
]
\addplot
coordinates{(1,2)(2,3)};
\addplot
coordinates{(1.2,2.2)(2.2,3.2)};
\end{axis}
\end{tikzpicture}
\end{document}
And lastly: You can save this cycle list with a name to reuse it with the cycle list name key:
\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotscreateplotcyclelist{foo}{
{blue,mark=*},
{red,mark=square*,mark options={fill=green}},
{mark=o},
{yellow,mark=+},
}
\begin{document}
\begin{tikzpicture}[]
\begin{axis}[only marks,
cycle list name=foo
]
\addplot
coordinates{(1,2)(2,3)};
\addplot
coordinates{(1.2,2.2)(2.2,3.2)};
\end{axis}
\end{tikzpicture}
\end{document}
You could as well specify the only marks key in each of the elements of that \pgfplotscreateplotcyclelist (or just in some).
\documentclass, the used packages and\begin{document},\end{document}. – Skillmon Jan 10 '18 at 19:28