Text alignment on top with multirow command

This is easily handled with the newly updated multirow command. There is an option that specifies vertical text alignment; put [t] for top alignment.

In your example you would write:

\multirow[t]{3}{*}{Targets} & Target 1 is long text with two lines & not reached\\

Here is the code that should yield the desired output:

\begin{table}[!h]
  \centering
  \caption{Title}
    \begin{tabular}{lll}
        \hline
        Name & \multicolumn{2}{l}{long title which goes over two columns}\\
        \hline
        Explanation & \multicolumn{2}{l}{Explanation which goes over two columns}\\
        \hline    
    \multirow[t]{3}{*}{Targets} & Target 1 is long text with two lines & not reached\\
        \cline{2-3}
        & Target 2 & reached\\
        \cline{2-3}
        & Target 3 & reached\\
        \hline
    \end{tabular}%
  \label{tab:test}%
\end{table}

P.S: Don't forget to add the multirow package.

Using \multirow (from the multirow package) pushes the contents down to the middle of 3 rows. Instead just drop the use of \multirow to have the cell top-aligned:

\documentclass[12pt]{article}
\usepackage{graphicx}% http://ctan.org/pkg/graphicx
%\usepackage{multirow}% http://ctan.org/pkg/multirow
\usepackage{calc}% http://ctan.org/pkg/calc
\begin{document}
\begin{table}[!ht]
  \centering
  \caption{Titel}
  \resizebox{.95\columnwidth}{!}{%
    \begin{tabular}{p{4.5cm}p{10cm}p{3.5cm}}
        \hline
        Name & \multicolumn{2}{p{\textwidth-3\tabcolsep-\widthof{test}-2\fboxrule}}
            {long title which goes over two columns}\\
        \hline
        Explanation & \multicolumn{2}{p{\textwidth-3\tabcolsep-\widthof{test}-2\fboxrule}}
            {Explanation which goes over two columns}\\
        \hline
        Targets % Don't use \multirow{4}{*}{Targets} here
            & Target 1 is long text with two lines exactly like this spans two lines & not reached\\
        \cline{2-3}
        & Target 2 & reached\\
        \cline{2-3}
        & Target 3 & reached\\
        \hline
    \end{tabular}%
    }
  \label{tab:test}%
\end{table}
\end{document} 

Instead of specifying the widths of the columns explicitly use the l specifier (which may require the array package). An example of its usage would be the following

\begin{center}
     \begin{tabular}{ | l | l | l | p{5cm} |}
     \hline
     Day & Min Temp & Max Temp & Summary \\ \hline
     Monday & 11C & 22C & A clear day with lots of sunshine.  
     However, the strong breeze will bring down the temperatures. \\ \hline
     Tuesday & 9C & 19C & Cloudy with rain, across many northern regions. Clear spells
     across most of Scotland and Northern Ireland,
     but rain reaching the far northwest. \\ \hline
     Wednesday & 10C & 21C & Rain will still linger for the morning.
     Conditions will improve by early afternoon and continue
     throughout the evening. \\
     \hline
     \end{tabular}
\end{center}

this will provide an output like this

Note the top alignment of all columns.

I hope this helps.