How to globally adjust horizontal spacing in table? @{length}

You just need to adjust the parameter \tabcolsep

\setlength{\tabcolsep}{.16667em}
\begin{tabular}{|p{2cm}*{4}{|p{1.5cm}}|l@{}|}
\hline
1 & 2 & 3 & 4 & 5 & 6\\
\hline
word & word & more words & more and more words & longtext longtext longtext & verylongword \\
\hline
\end{tabular}

You can use a group in order to keep the change local.

define a new columntype:

\newcolumntype{P}[1]{|@{\,}p{#1}@{\,}}

\begin{document}
\begin{tabular}{|p{2cm}*{4}{P{1.5cm}}|@{}l@{}|}