http://blog.humlab.umu.se/2006/01/the_endless_forest_1.html
"Gug hunting" is shorthand for "Having a relaxing amble through areas where you're pretty confident there are no gugs to be found, but you say you're hunting because it sounds better than 'goofing off.'" Ever since computer technology advanced to the point where it was possible to semi-realistically simulate actual sights and sounds, I've been fascinated by games where it's possible to sightsee, or even just sit in one place and watch the world go by. Here are some old and new favorites (many are multiplatform -- I've listed the platform I'm familiar with):
Powermonger (Amiga)
This RTS featured grazing sheep, birds flying overhead, and other charming pastoral touches. It's been a long time since I played it, but I think these humble details were there primarily to heighten the contrast between a village's everyday life and your own sudden invasion of it.
Aquanaut's Holiday (PS1)
Allowed you to pilot your personal submarine to the depths of the ocean and check out exotic fish, plus the occasional shipwreck. You could interact with fish by sending out sounds using the four shoulder buttons. If you got the right "combo," the fish would react with tricks. Some parts of the ocean are downright creepy -- even though there's no way to die in the game.
Tail of the Sun (PS1)
By the makers of Aquanaut's Holiday, and set in a similarly large world; but in Tail of the Sun, you actually have the ability to kill or be killed. Your caveman gets to see plenty of animals, foodstuffs based on cookies shaped like other foodstuffs, widely varying terrain and weather, ruins, and even caves. (SPOILER, of sorts: The world map is laid out like a female body... wink, wink, nudge, nudge.)
Everquest (PC)
I've mentioned before in the BYOND forums that my goal was to use the screenshot capture key to become the "Ansel Adams of Everquest." I abandoned this plan after I realized that I'd have to kill roughly a million rats in order to become powerful enough to survive stepping outside my home town. Mark my words, though: someday some dude is going to get rich selling framed lithographs of his most evocative video game screen captures to jaded big-city intellectuals.
Shadow of the Colossus (PS2)
In this world there are only 16 bad guys (and they have to be dispatched in increasingly annoying and improbable ways, but I digress). The rest is scenery and desolation. I'm not a real big fan of desolation in general, but SotC does it well.
Grand Theft Auto 3/Vice City/San Andreas (PS2)
It tickles me to reflect that the 3D GTA games, which have become the media's shorthand for everything that is wrong and evil about video games -- I'll save my pro-video-game-violence arguments for another day -- have always taken immense pains to portray the beauty and variety of nature. In fact, of all the games listed in this post, GTA: San Andreas probably provides the best "virtual gug hunting" experience.
Suggest your own favorite relaxing games in the comments!
[Updated Jan 28: I should also mention Neversoft's Gun -- great waterfalls! Also check the comments for games others have recommended.]