I remember when 192MB and 850Mhz was considered awesome. But by today's standards you'll find it extremely frustrating. If you do go ahead with this, I recommend you don't try to load X or anything graphical. Just stick with the bash shell.
The two distros I hear about the most for this application are Puppy Linux and DSL. I searched DistroWatch for old computers and it came up with those plus 19 more.
But you can get a new PC for $300 or a reasonable used one for $50. That would allow you to enjoy Linux properly.
"It should run on most computers, ranging from 64MB old PII 266 systems with pre-configured 128MB swap to the latest powerful boxes. 128MB RAM is recommended minimum for antiX. The installer needs minimum 2.2GB hard disk size. antiX can also be used as a fast-booting rescue cd." (http://antix.mepis.org/index.php?title=Main_Page)