The rule is that we do not bury a Rasha (wicked person) together with everyone else, or sit Shivah for him/her. However, under normal circumstances we never assume that a person is a Rasha, because even if we are certain that this person was guilty of many heinous sins, the possibility (or probability) exists that the person repented before passing away. After all, it only takes a single virtuous thought to do Teshuvah (repentance) and be transformed from a Rasha into a Tzaddik (righteous person).

A person who commits suicide, on the other hand, is defying G-d until the very last moment. G-d placed every person onto this world with a mission and a purpose, and completing this goal in the years which G-d has allotted is ultimately in the person's best interest. Suicide is saying that the life that G-d has given isn't worth living.

If, however, the person who committed suicide did not die instantly, we assume that the person repented in the last moments of life and we bury him/her in the cemetery and the relatives do sit shivah.

The strict law also does not apply if the suicide is a result of a mental or emotional illness (which is the case in the vast majority of suicides). In fact, there are those Halachic authorities that hold that as long as no one actually saw the person committing suicide in cold blood, we assume that the person had a nervous breakdown, and was therefore not responsible for his/her actions.

Therefore, although the law states that one does not bury a person who has committed suicide in the cemetery, and we also don't sit shivah for this person, practically speaking it is very rare to find a case which conforms with the abovementioned stipulations.