Output file contents while they change

You can use tail command with -f :

tail -f /var/log/syslog 

It's good solution for real time show.

If you want to show a short file, that fits on one terminal screen, and what is changing is possibly the whole file, you could use watch:

watch cat example.txt

Every 2.0s: cat example.txt                                Sun Aug  3 15:25:20 2014

Some text
another line

It shows the whole file every 2 seconds by default, including an optional header:

The option -d (--differences) will highlight changes from previous version of the output, or from the first version.

less has a follow mode similar to tail -f - just hit F when you have it open.