People

Ri, a common Korean surname, a variant romanization of Lee
Rí (rig), an ancient Gaelic word meaning "king"
Ri (pronoun), a gender-neutral pronoun in Esperanto
RI, an initialism of Rex Imperator (king-emperor) or Regina Imperatrix (queen-empress), used by those British monarchs who were rulers of both the United Kingdom and the Indian Empire

Places

Ri (administrative division), an administrative unit in both North Korea and South Korea
Ri, Orne, a commune of the Orne département in France
RI, abbreviation of either the Republic of Indonesia or, in the Indonesian language, Republik Indonesia
Rhode Island, a state within the US (postal abbreviation RI)

Raffles Institution, a school in Singapore
Refugees International, an international humanitarian organization
Rehabilitation International, an international disability rights organization
Rotary International, international organization of business and professional leaders focused on non-political and non-sectarian humanitarian service
Royal Institution of Great Britain, an organisation devoted to scientific education and research
Royal Institute of Painters in Water Colours, a society in the Federation of British Artists
Chicago, Rock Island and Pacific Railroad (reporting mark RI)
Tigerair Mandala (IATA airline designator RI)
Italian Radicals, a political party in Italy

Ri (prefix symbol), a binary unit prefix symbol
Referential integrity, a database concept
Refractive index of an optical medium (in physics/optics) is a number that describes how light propagates through that medium
Arterial resistivity index, a measure of pulsatile blood flow
Ring Indicator, a signal in the RS232 serial communications standard
Rhombicosahedron, a polyhedron, by Bowers acronym
Residual income, a financial profitability measure of a company
Reputation Institute, a research and insights company that analyzes the reputation of corporations and places
Rapid intensification, a phenomenon in which the wind speed of a tropical cyclone increases dramatically in a short period of time
Research infrastructure, national or international infrastructure open to scientists (e.g. CERN)
Research institute, an establishment founded for doing research

Ri (cuneiform), a cuneiform sign
Ri (kana), a Romanization of the Japanese kana り and リ
Ri, a unit of measurement in Japan and Korea related to the Chinese li
Rock Island District, a commuter rail line on Chicago's Metra (abbreviated as RI on maps and schedules)