Reading this question on meta, I thought it would be a good idea to have a question about altering core, that can be referenced. The idea is not have answers simply saying this is bad, but I was aiming for a question with an answer that will explain things a bit for new comers.
Why is it a bad thing to do?
If you think you really need to do it, what do you need to be aware of?
You know all this but simply have to alter WordPress, how do you do it?
I could probably for the most part answer this question myself, but I'm hoping one of you gurus can write up a really good answer, explaining things, all the details.
Update:
I added a new question as a CW link. I think the initial question has it's merits too, but for something we can use as a reference, we should have one that is a CW, so that's why I made a new question for the cause. I tried to make an introduction, but let the bulk explanation be formed as answers. We could over time consider making an answer with all contributions that I can mark as accepted answer to make it stick to the top.