The current fastest modems are the so-called "56K" modems
But, FCC has limited rates to 53K and due to hardware and line constraints average connection rate seems to be about 44K.
Rockwell/Lucent's K56flex and 3Com U.S. Robotics' X2 standards are incompatible 56K modems. Using one of each results in transmission rate of 33.6K.
V.90 modem standard solves K56flex vs. X2 problem. Get V.90 modem or upgrade K56flex or X2 modem with free "flash" memory software to make any modem V.90 compliant.
Most external modems are rapidly giving way to internal PCMCIA cards (often called "PC" cards)
About the size of a (thick) credit card
PCMCIA stands for "Personal Computer Memory Card International Association"
Organization chartered in 1989 to establish and maintain set of hardware and software standards for such cards