Three years ago, we looked at the decline in handwriting skills, both in alphabetic languages and with characters: "Cursive and Characters: Dying Arts". See also "Japanese survey on forgetting how to write kanji ", "The esthetics of East Asian writing", and several posts on "Character amnesia".
Before the advent of computers, cell phones, and other electronic devices which do our writing for us, it wasn't always this way. Penmanship was a discipline that students practiced assiduously, and calligraphy was an art that vied with painting for compositional excellence and esthetic appreciation.
Typed and printed writing is generally clear for any literate reader, but overt legibility was not always a desideratum for handwriting.
If you want to have some fun, do an image search for '"Thomas Aquinas" handwriting'. For example, look at this sample on this webpage (the language is Latin). St. Thomas Aquinas surely must be one of the most egregious offenders in Western history for illegible handwriting; his output seems even more opaque than much of Chinese grass script (草書; M cǎoshū, C cou2syu1, which Wikipedia states should be translated as "cursive script"). (Cf. "semi-cursive script" [also called "running script"], which is less devilishly difficult to decipher than grass script.)
As Stephan Stiller (personal communication) puts it:
One might well think of grass script as the world's first known write-only script. Note that grass-script is normally for the representation of Literary Sinitic (Classical Chinese), which requires more than a language model for a reader to understand, even in printed form. A write-only language is a programming language with the reputation that code written in it is difficult to comprehend. The most commonly given examples are APL and Perl; APL is old but Perl is widely used.
I sympathize with those who are frustrated when they try to read the handwriting of St. Thomas Aquinas and Chinese cursive script. People often complain that my chicken scratches are unreadable, even when I try to make them painfully neat and clear!