Apart from H55, all the chipset present in your query are basically designed for Intel Sandy Bridge processors and are having LGA 1155 socket. They support the Sandybridge i3, i5 and i7 processors like i3 2100, i5 2300, 2400, i5 2500 and 2500K, i7 2600 and 2600K.
H55 is designed to support the previous generation Nehalem based 1156 socket i3, i5 and i7 processors like Core i3 560, i5 630, i5 750 and 760 and i7 860K processors. H55 has already reached its EOL.
H61 is the cheapest among all the sandybrige motherboard chipset and designed mainly for HTPC and normal setup. They are having very less number of SATA and USB ports and normally only two ram slots with maximum of 16 GB ram support. Most of them are lacking USB 3.o support. They do have onboard Display output and can use the fused IGP of the Sandybridge processors but don't support overclocking even if the K series unlocked Multiplier based Sandybridge processors are plugged into it.
H67 is the bigger brother of H61 chipset and normally they offers more features compared to a H61 mobo. They can have 4 ram slots with 32 GB ram support, most of them are also having SATA 3 and USB 3.0 support. They are also having onboard Display output and don't support overclocking. This chipset is targeted to Mainstream audience.
P67 is the 1st performance oriented platform and when a K series processor like i5 2500K are plugged into it, it supports overclocking. Non-K processors like i5 2400 can be used with it but overclocking is not possible. The disadvantage is that it does not have Onboard display output and the fused IGP of SB processors get disabled when plugged into this chipset based mobos. You need a discrete graphics card for display.
Z68 is the most advanced of the all and it basically combaines the features of P67 and H67 chipsets. It does support overclocking of the K series processor and it has onboard display output so that the IGP of the SB CPU can be used. Apart from that it also supports a feature called SSD smart caching where a small sized cheap SSD can be used as a buffer between the HDD and Ram to improve Read/Write performance. Theoritically it can provide 4 times higher performance than a standard HDD.
Adding some more points since you guys are making it sticky:
1. Non K Processor + H61 mobo = Intel IGP Enabled with Onboard Dsplay + No Overclocking + Lucid Logic Virtue Software support with dynamic switching between IGP and dedicated GPU (if Plugged) as per application need + 2 DIMM DDR3 slot with max 16 GB support + SATA 3 + optional USB 3.0
Example: Core i3 2300 + Asus P8H61-M LE B3
2. K Series Processor + H61 mobo = Same result as case 1
Example: Core i5 2500K + Asus P8H61-M LE B3
3. Non K Processor + H67 mobo = Intel IGP Enabled with Onboard Dsplay + No Overclocking + Lucid Logic Virtue Software support with dynamic switching between IGP and dedicated GPU (if Plugged) as per application need + 2/4 DIMM DDR3 slot with max 16/32 GB GB support + SATA 3 + USB 3.0
Example: Core i3 2300 + Intel DH67VR-B3
4. K Series Processor + H67 mobo = Same result as case 3
Example: Core i5 2500K + Intel DH67VR-B3
5. Non K Processor + P67 mobo = No onboard Display + No Overclocking + No Lucid Logic Virtue Software support + 4 DIMM DDR3 slot with max 32 GB GB support + SATA 3 + USB 3.0
Example: Core i5 2400 + MSI P67A GD55
6. K Series Processor + P67 mobo = No onboard Display + Overclocking + No Lucid Logic Virtue Software support + 4 DIMM DDR3 slot with max 32 GB GB support + SATA 3 + USB 3.0
Example: Core i5 2500K+ MSI P67A GD55
7. Non K Processor + Z68 mobo = onboard Display + No Overclocking + Lucid Logic Virtue Software support + 4 DIMM DDR3 slot with max 32 GB GB support + SATA 3 + USB 3.0 + SSD Smart caching
Example: Core i5 2400 + MSI Z68A-GD55
8. K Series Processor + Z68 mobo = onboard Display + Overclocking + Lucid Logic Virtue Software support + 4 DIMM DDR3 slot with max 32 GB GB support + SATA 3 + USB 3.0 + SSD Smart caching
Example: Core i5 2500K+ MSI Z68A-GD55