You are talking about making the default class_bbcode.php from this line:
return "<a href=\"$rightlink\" target=\"_blank\">$text</a>";
And then modifying it to have this instead:
return "<a href=\"$rightlink\" target=\"_blank\"><span style=\"text-decoration:underline\">$text</span></a>";
Well the BBCode on this forum is totally standard. (ie default) Which makes it easier when update versions are released
Certainly sites using BBCode do not automatically have underlined links as standard
Obviously you can still underline your link ie: http://www.google.com this by adding [U] to the beginning and the same at the end, except with a preceding forward /
you can see all BBCodes available at TechSpot here:
http://www.techspot.com/vb/misc.php?do=bbcode
Personally I don't like the underlines on links, but I would prefer an underline shown once my mouse moves over the link (of which it doesn't)
Here you can find a basic BBCode guide (http://www.phpbb.com/community/faq.php?mode=bbcode)
Note:
Not all BBCodes are implemented (or "Modded") into the currently used BBCode at TechSpot ie I've been asking for [spoiler] Mod for some time now