How to break a long URL

It should be noted up front that the long-URL issues you are encountering can arise regardless of whether the URL occurs inside an enumerate environment or not.

By default, if a URL string contains a hyphen character, neither \burl of the breakurl package nor \url of the url package will insert a linebreak after a hyphen character. (This setting is chosen to avoid ambiguities over whether the hyphen character is a part of the URL string or not.) To override the default setting, load the breakurl package with the hyphenbreaks option or, equivalently, load the url package with the hyphens option set (and use the command \url instead of \burl, of course).

However, even with the hyphenbreaks/hyphens options set, overfull lines can still occur. An additional measure you may have to take is to issue the command \sloppy. This directive lets TeX expand the amount of interword whitespace (almost) arbitrarily to support its efforts to avoid overfull lines.

The following, modified form of your MWE shows how this works. The packages breakurl and url are loaded with the options hyphenbreaks and hyphens, respectively. Even so, the first two items in the enumeration, which use the \burl and \url commands, produce overfull lines. In contrast, the third and fourth items, for which the directive \sloppy is in effect, do not produce overfull lines. (By the way, in this MWE the scope of the \sloppy directive ends at the \end{enumerate} statement.)

\documentclass{article}
\usepackage{lipsum} % load paragraphs of filler text
\usepackage[margin=3cm]{geometry}
\usepackage[hyphenbreaks]{breakurl}
\usepackage[hyphens]{url}
\begin{document}

\lipsum[2] % generate some filler text (to show width of text block)

\begin{enumerate}
\item
svn co \burl{https://svn.xxx.ch/reps/yyyyyyyyyy/Publications/ABC-paper-2012/trunk ABC-paper-2012}
\item 
svn co \url{https://svn.xxx.ch/reps/yyyyyyyyyy/Publications/ABC-paper-2012/trunk ABC-paper-2012}
\item
\sloppy
svn co \burl{https://svn.xxx.ch/reps/yyyyyyyyyy/Publications/ABC-paper-2012/trunk ABC-paper-2012}
\item 
svn co \url{https://svn.xxx.ch/reps/yyyyyyyyyy/Publications/ABC-paper-2012/trunk ABC-paper-2012}
\end{enumerate}
\end{document}

None of the answers helped me out. My long url was placed in a footnote. After searching around I found a working solution here.

In my preamble:

\usepackage{hyperref}
\def\UrlBreaks{\do\/\do-}

The last line instructs the url-package which is loaded with the hyperref-package to additionally break at the characters / and -. The option breaklinks=true in hyperref can be invoked too but for me it had no effect.

The problem with breakurl package is that it seems incompatible with PDFLaTeX, and XeLaTeX. My colleague Dag Langmyhr pointed out that the url package is compatible with hyperref if it is loaded before the latter, and consequently

\usepackage[T1,hyphens]{url}
\usepackage[colorlinks,urlcolor=blue]{hyperref}

does the job more elegantly (breaklinks=true did also not work for me). This approach allows the normal \url command to be used when inserting the URLs.