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If it's a freebie host don't expect to have access to the raw logs, where you can see a record of every visitor that comes to your site, including spiders.
If it's a paid hosting service, you probably have access to the raw logs via an FTP client like WS_FTP which is available for free on the web.
What follows is only a small part of what mayor is coaching you on.
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I don't know if your host server is the same as mine, but when you're looking at those files from within your FTP client - the very first one (at the top of the list) should be viewable as a .txt file even after you download it to your hard drive. Just that first one, mind you.
That file shows the most current activity and is also the data that shows in your daily stats page when you view it.
Once the time period set by your host server (usually a week) runs out, that viewable .txt file gets converted by your host server into one of those .gz files and a new .txt file is started.
As you become better at evaluating access_log files you might want to keep tabs on that one as it shows traffic more incrimentally and not enmasse like the .gz files.
Myself, I download that one several times a day.
Just a thought.
Pendanticist.
You will find further information on spiders here in this forum. Use the WebmasterWorld site search to identify newer or "rogue" spiders.
When you look in your logs, generally, the respectable spiders look for your robots.txt file first. That should help you see the spider visits.