With tabbing
\documentclass{article}
\begin{document}
\noindent\vrule height2pt depth 2pt\hrulefill\vrule % to show the line width
\begin{tabbing}
\=\hspace{10pt}\=\hspace{10pt}\=\hspace{10pt}\=\kill
\>\> cat \> dog \> bird \\
\end{tabbing}
\end{document}

I refuse to show the result with too narrow distances.
An environment where you can specify the distances from the left margin and doesn't require the starting \>\>
\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\NewDocumentEnvironment{ftabbing}{m}
{
\marioscool_set_distances:n { #1 }
\begin{tabbing}
\tl_use:N \l__marioscool_preamble_tl
}
{
\end{tabbing}
}
\tl_new:N \l__marioscool_preamble_tl
\dim_new:N \l__marioscool_distance_dim
\cs_new_protected:Npn \marioscool_set_distances:n #1
{
\tl_clear:N \l__marioscool_preamble_tl
\dim_zero:N \l__marioscool_distance_dim
\clist_map_inline:nn { #1 }
{
\tl_put_right:Nx \l__marioscool_preamble_tl
{
\exp_not:n { \=\hspace } { \dim_eval:n { ##1 - \l__marioscool_distance_dim } }
}
\dim_add:Nn \l__marioscool_distance_dim { ##1 }
}
\tl_put_right:Nn \l__marioscool_preamble_tl { \=\+\+\kill }
}
\ExplSyntaxOff
\begin{document}
\noindent\vrule height2pt depth 2pt\hrulefill\vrule % to show the line width
% this one is for comparison
\begin{tabbing}
\=\hspace{10pt}\=\hspace{10pt}\=\hspace{10pt}\=\kill
\>\> cat \> dog \> bird \\
\end{tabbing}
\begin{ftabbing}{10pt,20pt,40pt}
cat \> dog \> bird \\
AAA \> BBB \> CCC \\
\end{ftabbing}
\end{document}

\rlap,\hbox to,tabbing,tabular, ... In order to give you the best answer, we would need to know some background as what do you want it for. Maybe construct a MWE using\hspace*and then say what should be modified? – yo' Nov 01 '14 at 12:55