That is absolutely possible.
What you need is some programming environment on the computer that supports reading from the serial port. This can be doné in most lprogramming languages both under Windows, on the MAC, and under LINUX.
Writing a program that reads from the serial port usually is not too complicated.
I have done it with Visual Basic .net (VB 2005), but almost any language will have the ability. My program reads the value of 16 potentiometers hooked up to the Arduino board.
It is also possible to have two way communication between the Arduino board and the PC, so for instance you could have the program on the Pc ask the Arduino borad to send information from your sensors when needed.
One important rthing you should be aware of is that you need the serial port on the Arduino board (the USB port) for the communication with the PC, and some sensors are also controlled / read with serial communication. You can not use the built in serial port for both at the sametime, so if you have sensors that need serial communication you should check the forum / playground / example code for how to use softserial communication. This is a way to implement an aditional serial port with two digital pins on the Arduino board and some software.
Good luck with your project.