Advanced Taxonomy Blocks makes use of the JQuery menu module to create extremely customizable blocks for browsing through single hierarchy taxonomies. Though the taxonomy menu module does something similar, if you use this module you will see that they are in fact entirely different in their approach.
Unlike taxonomy menu which directly ties the menus into the Drupal menu system, Advanced Taxonomy Blocks doesn't touch the menu system at all and therefore allows much more flexibility. This module ships with two default blocks: A block with all of the enabled vocabularies displayed by default (this can be customized to show only certain vocabularies) and a Forum block (I went ahead and threw this in since forums are built with taxonomy).
In addition to the two default blocks new blocks can be created with total control over which vocabularies are included, the path patterns (using pseudo tokens such as taxonomy/term/%tid ) that will be used (set per vocabulary per block) and much more. The beauty of being able to control the path in such a fine tuned manner is that you can create multiple blocks using the same vocabulary that send the links to different views (which would in turn receive the tid as an argument). You can also set each vocabulary within the block to show either a node count for all content types, or for only one particular content type, or no count at all.
Advanced Taxonomy Blocks is designed to work with single hierarchy taxonomies, which is to say that if terms have more than one parent I don't know how it will display (I have never tried it).