The web-browser from Opera Software is a highly featured application: web-browser, email-client,RSS reader, torrent-client… It can easily be installed from slackbuilds. It is proprietary software.
Slackbuild adress: http://slackbuilds.org/repository/13.37/network/opera/
If you want to very latest version, you can visit ruari's blog.
Alternatively, you can get a Slackware-compatible official release from Opera's download page. It comes with a script to install opera to a location of choosing (the default choice of /usr/local is good - if you try to install as a user other than root, it will recommend installing to $HOME/.local) as well as an uninstall script. However, opera includes no update mechanism - you will have to download and install new versions by hand.
Finally, one can use the script op2slk to download the latest Opera version and convert it to a Slackware package for later (un)installation.