So, I'm wanting to make a Runescape fan site. I'm curious as to how you guys feel would be the best way to grab high scores and adventure log avatars from the official Runescape website? I've seen it done many times before and I have not the slightest clue how I could achieve this.

I would actually do a few Google searches on this, because I'm not sure that Jagex would open up their Databases like that. There is probably another way to gather that information. It could involve something similar to an RSS feed. Actually, check that out, there may be a way to subscribe to the highscores via RSS and display them on your site.

Good luck with your forum!

Like this? http://pceasies.com/blog/2010/09/05/runescape-hiscore-api-in-json-format/

Or, you can use PHP to grab the hiscores: http://forums.zybez.net/topic/1239311-getting-data-from-the-runescape-highscores-with-php-and-mysql/#entry11347539