How can I make an enumerate list start at something other than 1?

You can change the counter named enumi, like this:

\begin{enumerate}
  \setcounter{enumi}{4}
  \item fifth element
\end{enumerate}

(If you have lists at deeper levels of nesting, the relevant counters are enumii, enumiii and enumiv.)

The enumitem package provides a simple solution to very many common problems that are related to minor tweaks of enumerate/itemize/description. In this case, you can use the start parameter. Also have a look at the resume parameter.

If you only want to alter the starting value, the easiest way is:

\documentclass{article}

\begin{document}

\begin{enumerate}\addtocounter{enumi}{41}
  \item This item is numbered `42.'
    \begin{enumerate}\addtocounter{enumii}{5}% This cannot be more than 25
      \item This one is ``numbered'' `(f)'
    \end{enumerate}
\end{enumerate}

\end{document}

While you can have six layers of nested list environments (itemize, description, enumerate), you can have no more than 4 of one type. The counters enumi through enumiv control the index of each item's label. You can increment (as shown) or decrement (add a negative value) all 4 levels.

Note, though, that this won't be entirely arbitrary. Levels enumerated alphabetically cannot have items after an item labeled 'z.' (You could, however, add a negative amount to the appropriate counter to get it back to the `a' label.)

(Now that I see the other answer, I wonder why I always opt for the relative \addtocounter rather than the absolute \settocounter?)