Category tags like drupal.org (Drupal 7)
There are a number of modules such as:


Nice Tags, here is an excerpt about it from the module's project page:


  ... improves seamlessly the UX for taxonomy tags input fields.
  
  No 3rd party JS libraries are required, as it works out of the box with jQ version shipped with Drupal.

Active Tags, here is an excerpt about it from the module's project page:


  ... adds a new option to free tagging taxonomies. If selected the taxonomy widget is replaced by a new jQuery enabled tag entry widget.
  
  Works with core Taxonomy module and Content Taxonomy module.
  
  This module came about through work on a site where some users found separating tags with commas confusing. Some users got it, and some didn't. This resulted in a site littered with concatenated tags. Wordpress has a similar tag entry mechanism where tags are entered separately. It has been implemented here using jQuery to rewrite the standard taxonomy entry form.



You can also use your taxonomies as tags as well if that's something you are interested in.