A non-database stats script would in my opinion be either unsecure or not powerful enough, plus it would take up much of system resources. Especially if your website is (becomes) popular. Text database is really not the way to go for a stats script (at least a serious one).
There are plenty of free stats scripts. Have a look at
http://www.extreme-dm.com/tracking/
This is a free (paid version also available) remotely hosted stats script. I use it on a few of mine websites and I love it.
Regards