Other Non-ligand-gated Ion Channels

Other Ion Channels (Wiki) 
This article is not in perfect English, but I have left it unedited. 
"Other gating include activation/inactivation by e.g.
second messengers from the inside of the cell membrane, rather as from outside, as in the case for ligands.

Ions may count to such second messengers, and then causes direct activation, rather than indirect, as in the case were the electric potential of ions cause activation/inactivation of voltage-gated ion channels.

Some potassium channels Inward-rectifier potassium channels: These channels allow potassium to flow into the cell in an inwardly rectifying manner, i.e., potassium flows effectively into, but not out of, the cell. This family is composed of 15 official and 1 unofficial members and is further subdivided into 7 subfamilies based on homology. These channels are affected by intracellular ATP, PIP2, and G-protein βγ subunits. They are involved in important physiological processes such as the pacemaker activity in the heart, insulin release, and potassium uptake in glial cells. They contain only two transmembrane segments, corresponding to the core pore-forming segments of the KV and KCa channels. Their α subunits form tetramers. 

Calcium-activated potassium channels: This family of channels is, for the most part, activated by intracellular Ca2+ and contains 8 members. 

Two-pore-domain potassium channels: This family of 15 members form what is known as leak channels, and they follow Goldman-Hodgkin-Katz (open) rectification.

Light-gated channels like channelrhodopsin are directly opened by the action of light.

Mechanosensitive ion channels are opening under the influence of stretch, pressure, shear, displacement.

Cyclic nucleotide-gated channels: This superfamily of channels contains two families: the cyclic nucleotide-gated (CNG) channels and the hyperpolarization-activated, cyclic nucleotide-gated (HCN) channels. It should be noted that this grouping is functional rather than evolutionary.

Cyclic nucleotide-gated channels: This family of channels is characterized by activation due to the binding of intracellular cAMP or cGMP, with specificity varying by member. These channels are primarily permeable to monovalent cations such as K+ and Na+. They are also permeable to Ca2+, though it acts to close them. There are 6 members of this family, which is divided into 2 subfamilies. 

Hyperpolarization-activated cyclic nucleotide-gated channels

Temperature Gated Channels: Members of the
Transient Receptor Potential ion channel superfamily, such as TRPV1 or TRPM8 are opened either by hot or cold temperatures.

By ions
Chloride channels:
This superfamily of poorly-understood channels consists of approximately 13 members.

Potassium channels
Voltage-gated potassium channels 

Calcium-activated potassium channels 

Inward-rectifier potassium channels
Two-pore-domain potassium channels:
This family of 15 members form what is known as leak channels, and they follow Goldman-Hodgkin-Katz (open) rectification.

Sodium channels
voltage-gated sodium channels
epithelial sodium channels (ENaC)

Calcium channels 

Proton channels
Voltage-gated proton channels 

Non-selective cation channels: These let many types of cations, mainly Na+, K+ and Ca2+ through the channel.
Most Transient receptor potential channels"