What is the most difficult conversation to have with an employee but one that really needs to be addressed?

Intimate behavior items, such as hygiene, presentation, and inter-personal relations.

In addition to the discharge conversation.

I like Wayne's list, but, for me, the most difficult is the discussion when the job is not a fit, but is highly desired by the employee.

Difficult conversations with employees create opportunities to improve their productivity, cut ties with them when it makes sense for your company, and offers opportunities to improve the work environment at your company.

I would count the following among the most difficult conversations to have with an employee:

1. The performance improvement conversation with a long-time employee (i.e., you need to improve or your future here is no longer certain).
2. The separation conversation. When an employee is no longer adding value to your company it is time to part ways. The key to making this easier it to be sure he or she becomes self-aware that he or she is not performing to expectations. This can be done by having he or she explicitly define for you what their accomplishments have been, and where they have not lived up to expectations and goals (and why).
3. A conversation that conveys with an employee that he or she is viewed by co-workers as a "squeaky wheel". An employee may be doing their job, but how they do it, and how they interact with other employees in general, is affecting the productivity of co-workers. Many people who are "squeaky wheels" are not aware they are affecting the productivity of others. They need the "we are all a team talk" which conveys that and when he or she affects a co-worker he or she is affecting the success of the company.
4. In general, all difficult conversation with an employee, including hygiene, are made easier the better you know an employee. What makes them tick? What affects his or her productivity? How does he or she get along with others at work? Note that employees change over time, so you need to stay "in tune" with them. As soon as as you see the perceived ,or actual, productivity of an employee going the wrong direction be pro-active and find out why.

Again, the better your relationship with your employees the lower the probability you will need to have "difficult" conversations with them. If an employee is not taken totally off-guard by a conversation, then the actual difficulty of any conversation can decrease dramatically.

Easiest conversations are with employees that are disruptive, and they know it.

More difficult conversations are with employees that are trying, but they are over their abilities, and they know it.

Hardest conversation when employees are impacting others negatively, but DO NOT know it.

The hardest questions are those in which the problem is related to the employees personality rather than work performance (i.e. dress, attitude, mannerisims). It is easy to point to specific issues when it is work performance. However when it comes down to telling a nice person that they are just not fitting into the corporate culture that is a very personal statement to the employee. That is harder to work on with an employee as well as many times it is an abstract concept where actual work performance can be documented.