Why does underlined text not get wrapped once it hits the end of a line ?

In text mode, the \underline command will enclose its argument in a horizontal box, which doesn't allow linebreaks. Use the \ul command of the soul package instead.

\documentclass[12pt]{article}

\usepackage{soul}

\begin{document}

A sentence that is just included to fill the line. \underline{Some text with underlining.}

A sentence that is just included to fill the line. \ul{Some text with underlining.}

\end{document}

EDIT: As for why \underline works the way it does, see this entry in the UK TeX FAQ for starters. It would seem that Leslie Lamport (the author of LaTeX) implemented just a "quick fix", and that only later package authors came up with more satisfactory solutions for underlining. See sections 2 and 7 of the soul documentation to get an idea of how complicated things are.

The \ul command from the soul package has troubles with Umlauts -- the \uline command from the ulem package doesn't and therefore seems to be the better option for those not exclusively writing in English.