All three chipsets are very similar (especially the H67 and P67). Here are what I consider to be the main differences.
H61: No overclocking, No support for SATAIII (6.0 Gbit/s)
H67: No overclocking (some would say very limited), 1333MHz memory limit, can utilize on-die graphics
P67: No integrated graphics, can not utilize on-die graphics
Basically if you are thinking of purchasing one of these boards, then you need to ask yourself what you are going to be doing with that build. For example, if overclocking is your thing, then you definitely want to go with the P67. If you want something basic, then go with the H61. If you want a nicer HTPC and don't intend to overclock, then you probably want to go with the H67.