What kinds of systems can I put in place to gather feedback from my community? I preferably want a system that is open, public, doesn't require a special event to use, and allows for discussion from peers.
There are quite a few ways to gather feedback from the community.
This is the system StackExchange uses to gather feedback and features. It has an advantage as it is very public and gives more concrete ideas.
An example being "Can we have feature x?" and an answer being "No" with reasons why. Comments are absolutely essential here, as this gives a way to respond.
Forums and Discussion Software
Forums and discussion work for this as well. This has an advantage in the fact that is encourages discussion. Most software for this allow users to create polls (this helps distinguish between "I don't agree" and "This is spam".
Mailing lists are similar, but have the disadvantage of only applying to a smaller group.
Probably the least public way of showing feedback is a traditional feedback form. This usually involves a HTML form of some type which sends an email.
This has the advantage of having private conversations, but this is usually only one way and usually the least action results from this.
I love the Meta system that Stack Exchange uses - every site gets a meta site, where issues can be freely discussed. It's open, public, and allows feedback from peers. People also tend to use this to raise issues about the mechanics of your site, etc. Basically a 'site about the site', or a 'forum about a forum'. You could even have a subforum/section instead of a full-blown second forum.
meta.moderators.stackexchange.com is the meta for this site, for example.