Matt Cutts answered a very similar question some time back in this video response.
In short, it's not a problem having these date/category pages, provided you've got them formatted correctly. Basically, just make sure that on each of these pages, you're only showing the heading and a small snippet; usually a paragraph or two and maybe an accompanying image.
If you're doing this, search engines have no issue understanding that it's essentially an aggregation page rather than duplicate content. If you're unlucky enough to be working with a CMS that just dumps then entire posts onto each category/tag page then you're definitely playing with fire!
If you're using Wordpress, often the simplest way to go about doing this is using the "more" tag which you'll find at the top of the text area when writing a post. Clicking that button will add into the HTML which cuts the snippet off at that point and provides a "read more" link to the full article. Here is a link to more info about it, note that current versions of wordpress do look different to these screenshots; you're looking for a button that just says "more", rather than the icon they use here.
The best way to deal with it is to update your template to automatically cut it off at a certain length for you, it just depends on whether you have access to a dev to make this change.
