INxx types are naturally and deeply introspective, which makes them reflect and over-examine their inner world which makes them prone to depression.
A guy on another MBTI forum summed this up quite well:
Either INTP or INFJ. INTJ and INFP, I think, are more relieved by thinking about it - they have introverted emotions. INTP/INFJ.. their emotions are more contingent on extraverted states of affairs; and to the extent states of affairs are less then ideal, this creates an impression of no escape. With INFP/INTJ, suicide is a matter of escaping an internal conflict, and not an external conflict. When the conflict is centered internally, it is easier to keep steady. INFP/INTJ have a consistent, constant nagging depression; a particularly neurotic dysthymia. When INTP/INFJs are fucked up, they are riding a train which is out of control, and are subject to the whims of their environment.. this exists to the extent they are invested in an ideal external state of affairs which is unattainable and unrealistic; you could call it a psychotic fantasy.
INFs are the most feeling-oriented of all the types, emotions being the core of their internal world - the most sensitive and emotional of all the types. In general, I'd say INFPs are the most likely to have thoughts of suicide, while INFJs are more likely to attempt it.