Gi protein
Gi is the G protein that turns the volume down. It is the counterweight to Gs: when a Gi-coupled receptor is activated, Gi clamps down on the cyclic-AMP-making enzyme, so the internal cyclic-AMP signal falls and the cell quietens.
The activated Gi alpha subunit binds GTP, separates from beta-gamma, and inhibits adenylyl cyclase, lowering cyclic AMP and therefore protein kinase A activity. The freed beta-gamma subunits do real work too: in the heart they open potassium channels (slowing the heartbeat) and in neurons they close calcium channels (reducing neurotransmitter release). The "i" stands for inhibitory.
Many clinically important receptors are Gi-coupled: mu-opioid receptors (morphine), alpha-2 adrenoceptors (clonidine), muscarinic M2 receptors in the heart (acetylcholine, slowing the pulse), dopamine D2 receptors, and adenosine A1 receptors. This is why opioids dampen neuronal firing and why vagal acetylcholine slows the heart — both recruit Gi. Pertussis toxin blocks Gi by chemically modifying the alpha subunit so it can no longer be activated by its receptor.
The same receptor type can couple to Gs in one tissue and Gi-like proteins in another, so the net effect on cyclic AMP — up or down — is tissue-specific.