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It is still quite normal to have googlebot as the most frequently visiting spider, but a well established website really should have lots of visits from other search engines. If many websites are pointing to yours it ought to be well known by search engines.
The internal linking structure may be a factor. It is an advantage to have a flat hierarchy with all pages only one or two clicks away from your frontpage.
And how complicated is your html? Some spiders may be reluctant to follow internal links if you have large or complicated files with deeply hidden links.