Align text on top of a framebox

Here is a short non-TikZ solution.

\documentclass{article}
\usepackage{color}
\begin{document}
\makeatletter
\fboxsep8pt
\fboxrule0pt
\@for \next:=A,B,C,D,E\do{
 \fbox{\next}%
}

\vspace{-3pt}
\fboxrule1pt
\fboxsep7pt
\@for \next:=A,B,C,D,E\do{
 \fbox{\color{white}\next}%
}
\makeatother
\end{document}

It will also work if you change the \@for to \@tfor as follows:

\@tfor \next:=ABCDE\do{
 \fbox{\color{white}\next}%
}

I prefer expl3 to tikz for repeating things:

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\idbox}{}
  {
   \framebox[4.5mm]{\vrule depth 1.25mm width 0pt height 2.5mm}
  }
\NewDocumentCommand{\idnum}{m}
  {
   \begin{tabular}{@{}l@{}}
   ID~Number\\
   \prg_replicate:nn { #1 } { \idbox \hspace{3pt} }
   \end{tabular}
  }
\ExplSyntaxOff
\begin{document}
\idnum{5}

\idnum{7}
\end{document}

A tabular environment is just the more convenient way to align objects. A tabular free macro could be

\NewDocumentCommand{\idnum}{ m }
  {
   \vbox:n
     {
      \hbox:n { \strut ID~Number }
      \hbox:n { \strut\prg_replicate:nn { #1 } { \idbox \hspace{3pt} } \unskip }
     }
  }

But I don't see why one should prefer this approach to the simplicity of a tabular.

It's all Yiannis' fault by mentioning 'non-TikZ' solution :-) Here is a TikZ solution...

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\foreach[count=\xi] \x in {A,...,F}
{
\node[label={[inner sep=1mm]90:\x},draw,inner sep=3mm] (\x) at (\xi,0) {};
}
\end{tikzpicture}
\end{document}

Positioning can be changed via modifying at (\xi,0) with at (0.8*\xi,0) and similarly box sizes can be changed by the second inner sep option. (First defines the distance of the letters from the box.)