There literally are dozens of PC based data acquisition systems that use the serial port to interface to the PC.  Many of these may be used with programs written in any Windows language, including Visual Basic^® (my primary interest).  Some use proprietary protocols, and are meant to use applications that are furnished with the hardware.   While this second category is useful, I will not go into details on their operation, though I will include links so that you can seek more information -- if this strikes your fancy.

Systems that use serial interfaces range in performance from low, up to a few hundred Hz, to fairly high, 100 KHz or higher are possible, if the system employs sufficient memory to buffer all data acquired in real time.  A simple calculation shows what raw acquisition rate is the maximum that can be achieved by systems that must use the serial port to send acquired data to the PC in real time.  The maximum serial port speed for normal 16550A UART based serial ports is 115 Kbits/s.  This results in a raw maximum real time acquisition rate of 11.5 K bytes/s.  Practical implementations will restrict this to 10 K bytes/s (or less), largely dependent on the capability of the PC that hosts the application software.  This is roughly an order of magnitude higher performance than can be reached by most parallel port based devices (see Other Parallel).

(1/2014)  I have been creating a number of very inexpensive data acquisition projects that are based on different Arduino platforms.  Arduino provides a very natural development environment and it can be perfect for one-off or limited production test and measurement systems.  I have a number of Arduino examples in my book (see the next paragraph).

Many manufacturers of serial port based A/Ds provide ActiveX controls and/or C based libraries for application programming.  Those that are not furnished with programming controls or libraries, and that don't implement a proprietary data format, can be interfaced using the methods that I describe in my book, Visual Basic Programmer's Guide to Serial Communications.  These can range from the Data Logger example in my book that uses a DVM, to much higher performance applications. 

I have created an ActiveX control for B&B Electronics 232SDA series of Data Acquisition Modules.  Click this link to go to my 232SDA page.