If you're receiving very good amount of traffic then it will be a very bad idea to no-index tags, because you'll not receive any more traffic if you do so. i think you understood what it means by no-index, search engines will not index your tags.
For any site there would be 2 types of navigation:
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through categories.
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through tags.
Most People recommend using only one as a primary navigation and de-index other, since indexing both will cause duplicate content. There are some gurus like Yoast.com who recommend de-indexing both, which is the rule i'm following now.
So, i explained you what happens, if you feel that you're getting more traffic through tags, then you should de-index categories or viceversa.
If you need to index both, then i recommend you to wait for other pro members suggestion.