I use a few different stat programs, my fav though, and the one I mostly use is Awstats. Love it! The stats are great! Delecia
I would recommend Google Analytics, it is free and it works pretty much as good as any other software out there. Nik
I agree with Nik. Google analytics is free and gives you many tools to customize your tracking. You can also link it with your google adwords account which is a new feature. It will help optimize adsense and adwords with you website.
Google Analytics stinks because it doesn't work in real time. You can't see any of your data on any particular day until the following day. I use statcounter.com and I use strictly the free version. It is enough for me. You don't need tons of log space. That is unless you want to keep stats for months and years. But why would you? Personally, I just use the stats to keep track of the general trend of my traffic. As long as I can see it trending upward, I'm happy. If it's trending downward then I want to see why. Statcounter gives me all the information I need to do this.
AWStats, by far the most info for tracking and reporting purposes. Standard equipment on most CPanel hosting accounts. Using ?TID=anyname after your URL gives targeted referrer results. Especially handy if you send a link by email and want to track any clicks. Also if you run multiple ads in one place, each ad can have it's own referral ID.
I am using statcounter.com and google analytic ... And as I think these good enough to check traffic ...
I'm not so sure about other softwares but I use Google analytics. It's pretty detailed and it's simple to use, also I think it's the best one so far. But if you don't want that, you can try other free softwares for tracking. I'm sure you can come up with more from the search results.