Vestibular Unisinos is a strange little Brazilian flash game in which you must reunite a stray school desk with a group of its fellows in a series of unlikely settings. Like other games of this type, you must click on different elements on the screen to make things happen. I'm not really sure why this game exists -- I think it's something about promoting university admissions tests. It's quite a nice game, really.
Portugese only, so get your help and hints at Nordinho.
Save the Kiddo is another classic Samorost-style game from the creator of Sangar Sabriina and Sabrina in North Pole. There's only one level, but it's nicely done.
There's a link at the top of the page to the site's own forum, with hints.
Under One's Wing, also referred to as Shanabea (I think that's actually the creator's name), is a very lovely game. It is reminiscent of Shift in the way you must progress by making a forest grow and move bit by bit. The game has several levels, all of them gorgeous, and there's more to it than just random clicking. There are hidden spots which you must unlock for a different ending, and if you just move along to the next level as fast as possible, you'll miss them. The game is in Japanese only, so the plot is a mystery -- but it's so nice to look at.
Get help at the game's post at lazylaces.
The Foonbox Arcade at Foon.co.uk boasts a couple of excellent games, Hapland and its sequel Hapland 2. Both are single-level games, but they are quite complex, and have the interesting feature that a single wrong move will doom you, requiring you to reset and try again. There is also Escape from Rhetundo Island, which is a slightly different kind of game requiring quick reflexes and precise timing rather than reflection and puzzle-solving. Frustratingly, a mistake at any level in this game will require you to replay all levels, and many trials are usually required to solve a level. But I throw it out there for the sake of completeness.
Here are some links to help you along: Hapland walkthrough; Hapland 2 walkthrough; Milkandcookies thread on Escape from Rhetundo Island.
Industry is a cute game inspired by Hapland. A very fun, nicely done game with the same cleverness and sense of humor as the Hapland series. Originally only four levels, a bonus fifth level was added later --
UPDATE 07/15/06: That link is no good. Here is a complete Industry walkthrough with all five levels, located at Flashtrofe, the creator's website.
Up next: Interactive eye candy.