Tags help to categorize your posts with sites like Technorati, so yes, they may provide a benefit in attracting visitors.
Tag archives on your blog itself also provide search engines pages of similar content to index — in addition to simple category archives — which provides yet another entry point for visitors.
The way I look at it, categories & tags work together quite well.
Categories are like folders. Say you have these folders: Current Events, Technology, Meta, and Sports.
Those are broad; tags let you get more specific and allow you to connect content posted in one category with content in another.
For instance, you might have posts in the Technology cat about WordPress plugin releases you are interested in. Such posts may be tagged “WordPress, plugins” or so. And you may also have in your Meta category a post describing the plugins you are currently using on your own blog — again, the same tags would be used.
The depth of organization is entirely up to each user, but having categories & tags together provides a very powerful framework for organization, in my opinion.