From a very high level view, to me it seems there are generally 2 types of Project Management tools:

1. Traditional issue trackers like Fogbugz, JIRA, BugZilla, Trac, Redmine etc.
2. Virtual card boards / agile project management tools like Pivotal Tracker, GreenHopper, AgileZen, Trello etc.

Sure, they overlap in one way or another, e.g. Pivotal Tracker tasks can be imported to JIRA, GreenHopper itself is implemented on top of JIRA issue base etc. but I think one can still see the difference in orientation between those two types of tools.

Traditional issue tracker seems to be used even in companies otherwise doing agile project management. My question is, why do they do that? I also feel that we should use an issue tracker in my company but when I'm thinking about it, I'm not actually sure why should we need it.

For example, Trello development seems to be managed by using Trello itself (see this virtual wall) even though they have access to Fogbugz, one of the best issue trackers around. So maybe we don't need traditional issue tracker when we'll be doing 100% of our work in an agile manner using one of the agile PM tools?