I am a frequent user of MathOverflow, which I understand currently uses a previous version of Stack Exchange software. As such I understand that the present feature request may have trouble making its way to me. I posted the following to the meta page there, and it was suggested here would be a better place for it. It is aimed at the developers of Stack Exchange.
At first when I began using MO, I didn't mind the diversity of topics listed on the homepage, but as it has garnered more and more users, of diverse backgrounds, interests, and abilities, I find myself (a) less interested in questions presented to me when I log in, (b) less able to elicit answers from knowledgeable people in my field (which I think is just a reflection of their own frustrations with (a)), and (c) less inclined to want to do much about it. I am afraid that the sprawling, accept-all-comers, diverse nature of the site has led it to be too vast a forum for me to function with efficiently. Wasting time is all well and good, but everyone's patience has its limits.
There are tags, which one can use to filter out unwanted entries and also to highlight one's interests. I have selected several in both categories, but again due to the sprawling nature of the site, managing these continually is more hassle than I'm willing to undertake. There are duplicates, or closely related tags, and there are new tags coming up often. If I feel like the utility of the site is diminishing, I am less likely to invest time sculpting my experience by fussing over tags, which don't seem to help much anyways.
So here's a simple feature request (simple to request, not so to implement =]). Have the stack exchange software track which questions I view, which questions I answer, and which questions I ask, as well as an weighted undirected graph connecting tags which appear in the same question with the multiplicity of their common appearance. When I log in, order questions not only by chronological statistics, such as recent activity, but also based on my perceived interests, as measured by the correlation of my interaction with the website to the aforementioned graph (I could be more specific here, but there are many intriguing ways to do this).
There are some downsides to such a proposal, so I suppose it should be an option users can turn on and off. But I fear as it is, MO has jumped the shark for most selective, research-oriented askers and answerers. Without a way of automatically tailoring content, the site is just going to get unusable.
I'm sure the site's creators know that I think it's an excellent enterprise, and a service. I only offer this functionality request because I think it will help make the site useful for everyone.