Yes, it is possible.
There are three very interesting ways to record the information generated by Arduino.
Computer (via Serial RS-232 or Ethernet)
That’s the most basic way. You turn on the Arduino on a computer (via Serial RS-232) and make a program (simple script) that connects to the Arduino and saves the information in a text file. Suggested languages for this: Processing, Python or Groovy.
SD card
You can store information on Arduino using an SD card. There are modules, Shields and even Arduinos that already comes with an input to an SD card. In addition, existing libraries for writing and reading are very simple to use.
Notes on using SD with Arduino
Scadabr (Modbus)
Another very interesting option is to use Scadabr. Scadabr is a Java WEB application (to be run in Tomcat). This application can interpret several protocols, one of them being called Modbus (via Serial RS-232 or RS-485 or via Ethernet). So, you use a Modbus library in Arduino, turn on your Arduino via Serial on your computer with Scadabr and configure Scadabr to receive information from Arduino. The great advantage of this approach is that Scadabr can be used for various Arduinos and to log in the most different types of information. The sky is the limit.
Scadabr uses the Derby (Apache) database and it records the information. It is very simple to obtain a period of time. It even has graphics ready.
To give you an idea of the power of the combination of Arduino + Scadabr, in the company I work the maintenance team has developed a solution with this combination that allows you to reconnect an electric sub-station using the Scadabr.
Summary
If your Arduino can run near a computer and the problem you want to solve is punctual, go on Computer option via Serial. You’ll solve this very quickly.
If your Arduino should run away from a computer and you don’t have time to connect it via Ethernet or RS-485, then go by SD card option.
If you want a solution to suit various Arduinos and other types of devices that talk Modbus, go by Scadabr.
updated the reply with some more information. They may be useful.
– cantoni