Good topic. This was my area of expertise when I worked on mainframe computers and distributed servers. Interestingly enough, this is the big area of focus on the internet, collecting data about activity, then making use of that data for whatever (marketing, spying, theft, building dossiers, or, as the cover story goes, quality assurance metrics to improve upon your web experience).
Okay, back to Arduino data collection...
Indeed, I find myself in the middle of this with almost every project. This would require a libray implementation, where a data collection can be instantiated, a few calls for adding data to the log, and controlling when the loggin occurs (start/stop, or criteria thereof).
Results can be directed as pointed out, to a serial connection, for immediate display, though that would require some type of PC connection, transmission mode, perhaps an intermediate server, or non-computer display (such as those for home weather stations). In fact, a home weather station, with an outdoor data module and indoor display module, seems to be a very nice model for this type of activity. I have thought about getting a complete home weather station, and then building my own interface for acquiring the data, performing the analysis and visualization.
One should also consider use of an attached SSD for data storage as an alternative to a real-time connection. Keep in mind that in the limited memory space of the Arduino, data collection is indeed a luxury item. Other micro-controller boards, such as the ARM based unit, would be better equipped for this type of activity.