I'm not sure about *any* new entries... that could get a little overwhelming in terms of notifications, but try Logwatch... it's the bread and butter of log file monitoring and has several levels of detail in terms of the e-mails it sends to you, as well as how frequently it sends those e-mails.
I use it for maintaining an Apache mirror and it warns me about security concerns (script kiddies), partition usage, http errors, aggregate download size... fairly basic but helpful.
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