The following examples are using \centering instead of environment center, see question "When should we use \begin{center} instead of \centering?" for details.
\showlists can be used to analyze the spacing:
% configuring, how much is shown by `\showlists` or `\showbox`
\showboxdepth=\maxdimen
\showboxbreadth=\maxdimen
\documentclass{article}
\begin{document}
\vspace*{0mm}
{\LARGE\centering Title}
\showlists
\end{document}
Result:
### vertical mode entered at line 0
### current page:
\write-{}
\glue(\topskip) 10.0
\rule(0.0+0.0)x*
\penalty 10000
\glue 0.0
\glue 0.0
\glue(\parskip) 0.0 plus 1.0
\glue(\baselineskip) 0.0
\hbox(12.0+0.0)x345.0, glue set 311.69482fil
.\hbox(0.0+0.0)x0.0
.\OT1/cmr/m/n/17.28 T
.\OT1/cmr/m/n/17.28 i
.\OT1/cmr/m/n/17.28 t
.\OT1/cmr/m/n/17.28 l
.\OT1/cmr/m/n/17.28 e
.\penalty 10000
.\glue(\parfillskip) 0.0 plus 1.0fil
.\glue(\rightskip) 0.0
total height 22.0 plus 1.0
goal height 550.0
prevdepth 0.0, prevgraf 1 line
Thus the page contains as additional white space elements before the title:
\topskip, it is a parameter that helps to align the first lines on the pages. It is only automatically added at the top of the page. On this page, however, there is not a "first line" to align. Thus it can be set to zero.
\parskip, here 0pt plus 1pt, but it might be different.
\baselineskip, here 0pt, because the next line is over large (\LARGE).
The following example avoids these white spaces:
\showboxdepth=\maxdimen
\showboxbreadth=\maxdimen
\documentclass{article}
\begin{document}
\begingroup
\setlength{\topskip}{0mm}% \topskip is set to zero
\vspace*{0mm}%
\setlength{\parskip}{0pt}% \parskip is set to zero
\nointerlineskip % avoids addition of \baselineskip before next line
\centering
\LARGE
Title
\par
\endgroup
\showlists
\end{document}
Result:
### vertical mode entered at line 0
### current page:
\write-{}
\glue(\topskip) 0.0
\rule(0.0+0.0)x*
\penalty 10000
\glue 0.0
\glue 0.0
\glue(\parskip) 0.0
\hbox(12.0+0.0)x345.0, glue set 155.84741fil
.\glue(\leftskip) 0.0 plus 1.0fil
.\hbox(0.0+0.0)x0.0
.\OT1/cmr/m/n/17.28 T
.\OT1/cmr/m/n/17.28 i
.\OT1/cmr/m/n/17.28 t
.\OT1/cmr/m/n/17.28 l
.\OT1/cmr/m/n/17.28 e
.\penalty 10000
.\glue(\parfillskip) 0.0
.\glue(\rightskip) 0.0 plus 1.0fil
total height 12.0
goal height 550.0
prevdepth 0.0, prevgraf 1 line
Thus the title hits the top of the text area. It can be visualized by option showframe of package geometry:
\documentclass[a5paper]{article}
\usepackage[
showframe,
% smaller image for answer in TeX.SX
paperwidth=5cm,
paperheight=5cm,
margin=5mm,
includeheadfoot,
]{geometry}
\begin{document}
\begingroup
\setlength{\topskip}{0mm}%
\vspace*{0mm}%
\nointerlineskip
\setlength{\parskip}{0pt}%
\centering
\LARGE
Title
\par
\endgroup
\end{document}

\centerwhich actually starts the center environment, which is a list.\vspace*{}puts an invisible box on the page and so the space before this list is no longer discarded at the start of a page. Better use{\LARGE\centering Title \par}. – Ulrike Fischer Jan 31 '14 at 12:23