Issue tracking systems

Major issue tracking systems

Proprietary ones and/or paid services
Will not cover those, it is mainly a source of frustration to me: they tend to be broken (perhaps not even worth listing: virtually everything that can be broken is broken at least in some of those) with no hope for improvement, yet managing to get sold and used in companies. I can go on complaining, but it would not be of much use.
Public services
Such as GitHub, SourceForge, Bitbucket, etc. Those are actually handy for hobby projects, though GitHub will probably look in a decade as SourceForget looks now: those fancy things don't seem to last long, though GitHub has plenty of apparent flaws even now: particularly in UI, and being centralized. Still, GitHub is used by plenty of rather large and nice projects as their primary BTS (and hosting, too). Perhaps it is worth highlighting Bitbucket (and Atlassian in general), where every tiny bit is terribly broken, and it'd keep spamming you if you ever [manage to] register there; extremely frustrating, and a few different feedback mechanisms are also broken.
Python, 3-clause BSD. A somewhat minimalistic system. Does not support multiple projects nicely (single-project system hacked to host more than one project), features are rather limited, not that easy to deploy properly. Though deemed good enough (and used) for large projects such as GHC.
Perl, MPL. Seems to be nice for larger projects such as GNOME, but perhaps not so nice for using in a relatively small company (or small hobby projects). User interface is not that handy. Apparently a nice and solid system overall, yet I am just avoiding it. Though as of 2020, there's a new UI full of private use unicode code points, and partially broken functionality without JS.
Ruby, GPLv2. Many features out of the box, pretty nice overall. Though markup is not good, mail notifications (their headers, in particular) are a bit broken for a long time, and it is rather hard to deploy properly.
Python, MIT. Supports email seemingly well, the web interface is quite clean and simple, JS-free, has fine documentation, relatively easy to install nicely. Though apparently the documentation is outdated: pointing out that it is in Debian repositories, while it is not anymore (well, it is in oldstable), and the last release at the time of writing (2017-11-30) is almost two years old. Hence no automated security updates and awkward manual installation; risky to deploy overall.
Mostly Perl, GPLv2. Very lightweight web UI, mail-only updates, actively used and maintained for 23 years now. Same issues as with most of the BTSes though: not in repositories, rather cumbersome manual installation, configuration, and maintenance. debbugs git repository is perhaps the primary source for its documentation (and sources).
Ruby, Go, JS; MIT for the community edition. Sluggish JS-based UI (as of 2022, pretty much unusuable in Firefox, though was very slow for years before that too; apparently it uses the Vue.js framework) with annoying animations, suggested installation method involves curl | sh, the website is full of marketing texts and broken markup with little focus on technical details, only minimal mail integration. Quite bloated, includes a CI service. Not sure why, but seems to be pretty popular at the time of writing (the end of 2018). Though it's rather a software forge, not just a BTS.
Perl, AGPL-3.0+. Similar to a mailing list archiver, but git-based: instead of server sending messages to subscribers, subscribers are supposed to pull it (via NNTP, Atom feed, WWW, or to mirror it as a git repository). I haven't tried to use it beyond reading archives produced with it, but it looks nice.
Go and JS, MIT. Along with derivatives, appears to be a reasonable option and fairly popular, as of 2024. Consumes notable server resources, says that it requires JavaScript (though seems to work fine for basic usage without that), apparently for-profit since 2022, but there is the Forgejo fork.
There is much more in the Wikipedia Comparison of issue-tracking systems and Comparison of project management software. Most of those are pretty bad.

Common issues

Other approaches

Common models and gateways

There are various attempts to integrate different programs and protocols (e.g., by using common models provided by RDF ontologies such as SIOC, all kinds of APIs and gateways), but they are not used any widely.

Distributed issue trackers

There are less common issue trackers that are distributed, like bugs everywhere. Perhaps worth trying, the description looks nice. ikiwiki can be used as such a system, in addition to having a web interface for reading, search, and editing. Simply a set of files (possibly hypertext-capable: org-mode, HTML, etc) may work, too.

TODO files and email

That's what I'm using the most, and perhaps it is the most reliable and simple way to manage tasks. Journaling can be used together with it or as an alternative. In my experience, over the years people occasionally ask to use some issue trackers, the ever-changing centralized IMs, voice calls, and/or just meet; those conversations are lost to email message archives, but can still be summarized in journal/TODO files. That's additional work, but helps to ensure that you have everything important written down, in one place, ready to be found when needed.