There is no way to just connect the right pins with each other. Serial and parallel (which includes also the centronics ports of the printer) are totally different concepts of data transmission. While serial ports transmit bitwise through 1 line, the parallel port has 8 data channels, which transmit simultaneously to make up 8 bits. I do not think that there are ready-made adapters!* If you really want to do this, it'll get ´lots of work and you need electronics skills.
If you have a palmtop, what about IRDA transmission?

*hmm, just found one, but it is not a real adapter, more kind of a translator. check out:

http://stores.yahoo.com/secureswitch/sertoparcon.html