There are a few other writing systems that were deliberately created. My favorite is the Cherokee syllabary [1].
A Cherokee man named Sequoyah ended up serving as a soldier in one of the early conflicts between English settlers and other Native American groups. In this case, his people were on the side of English settlers against rival tribes (see [2]), so he was serving alongside English soldiers in the conflict. He saw them reading and writing - something he couldn't do, since the Cherokee language had no written script at the time - and went "wait this seems like it would be pretty useful".
So Sequoyah, who until this point had never encountered a writing system, decides he's going to make one. He starts by trying to create a symbol for every word, but decides that's too difficult, so he switches to symbols for syllables instead. It took him ten years to finish it, but once he did, it was adopted by nearly every speaker of Cherokee within only a few years. It's still the primary writing system for the Cherokee language today.
IMO Tolkien's Tengwar is the closest to Hangul. The shapes of the consonants represent the place and manner of articulation, such that similar sounds look similar on paper. Vowels are written as diacritics above the consonants, with the result that each complete letter represents a syllable.
There are other syllabaries, both naturally occurring and deliberately created, but most of them don't show subpatterns that represent the sounds that make up each syllable. Cherokee looks a lot like the Japanese kana. Which is not surprising, because both are syllabaries designed to overcome the difficulty of a fully ideographic writing system (kanji in the case of Japanese).