Most levels of Zoombinis have some form of "penalty" system, where if you get something wrong, you either lose a Zoombini or increase the chance of losing whoever is left.
Are there any levels that don't have this penalty?
None of the puzzles are "all or nothing."
Each one of the puzzles has the chance to allow all or some of your Zoombinis through, and most can also allow none. This is mostly going by memory, but I believe Who's Bayou, Stone Rise, and Hotel Dimensia won't allow you to proceed with no Zoombinis. The first two are likely due to their other common trait (see below), while Hotel Dimensia apparently always accepts your first Zoombini.
Most puzzles also have a limit on the number of tries you get to solve it. Only three puzzles can result in instantly losing a Zoombini if you make a mistake: Titanic Tattooed Toads, The Mirror Machine, and Bubble Wonder Abyss. Oddly, Titanic Tattooed Toads is only in this category at the easiest difficulty; once you can swap lily pads, it's sometimes possible to get a trapped Zoombini through.
Similarly, two puzzles give you infinite tries to get the correct solution: Who's Bayou and Stone Rise, both of which allow unlimited rearrangement of your Zoombinis until you find a working solution (or determine one doesn't exist for your group). In all other puzzles, if you make too many mistakes, you will either A) start losing Zoombinis one by one until you complete the puzzle or run out of Zoombinis, or B) lose all Zoombinis that aren't approved (which might be all of them) once you run out of tries. No puzzles have an actual time limit, despite Hotel Dimensia using a clock to indicate your number of mistakes remaining.
Sources: http://www.gamefaqs.com/pc/563155-zoombinis-logical-journey/faqs/27636 and personal experience
As far as I can tell, level 2, with the stone caves, and level 4(?) with Captain Cage's Ferryboat, don't have this penalty. As far as "all or none" levels, there are none. Some levels are impossible if you have "bad" Zoombinis. In Captain Cage's Ferryboat, sometimes your Zoombinis don't have enough in common, and the Fleens level can be impossible. However, they still have either time or attempt penalties.