The current version of Brogue does not provide any system for challenge games or character "conducts" as some other roguelikes do. However, various ideas for challenge games have been proposed on the forums. This page lists some ideas for those who want to test themselves. Some of these challenges haven't been completed yet and might turn out to be almost impossible.
The aim of this challenge is simply to ascend in as few turns as possible.
Real Time Speedrun
Instead of aiming for fewest turns, aim for fewest hours. As broguerec does not keep track of elapsed time, you will have to record your run or be taken at your word.
This challenge has been completed (1.6.4 broguerec)
In this challenge game, you cannot use any scrolls, including Scrolls of Enchantment. Bear in mind that this means you have no means of uncursing equipment - equipping an item that you haven't soft-identified with a Potion of Detect Magic becomes extremely risky.
This challenge' has been completed (broguerec 1.6.4 broguerec)
In this challenge game, you are not allowed to eat. In order to survive, you will need to recruit an ally that can heal you in order to counteract starvation. You don't have much time to train an ally to heal, so your best bet is to use a Wand of Polymorphism to create a Dar Priestess (or preferably a Unicorn), then a Wand of Domination to make her your ally. Bear in mind that regeneration is switched off whilst you are starving; Rings of Regeneration become useless.
This page is related to version 1.6.4 and may be out of date.