Make different font sizes in a table align at top, not bottom

Inserting zero vertical space helps with aligning at the top:

\newcolumntype{V}{>{\vspace{0pt}}X}

Your complete example, with also \Huge text to see the effect:

\documentclass{article}
\usepackage{tabularx}
\newcolumntype{V}{>{\vspace{0pt}}X}
\begin{document}
\begin{table}
\tiny
\begin{tabularx}{\textwidth}{|>{\normalsize}V|V|>{\Huge}V|}
\hline
Foo & Bar & Baz\\
\hline
\end{tabularx}
\end{table}
\end{document}