List of foreign volunteers
Mixed nationality units: 

Historic: 60th (Royal American) Regiment of Foot. Composed of 'foreign Protestants'.
Boer foreign volunteers
Hohenlohe Regiment of France during the Bourbon Restoration.
International Brigades of the Spanish Civil War
Islamic Legion
Kenpeitai Auxiliary units consisted of regional ethnic forces that were organized in areas occupied by the Japanese.
King's African Rifles
The SS (particularly the Waffen-SS) made extensive use of foreigners during World War II. For more information, see: Waffen-SS foreign volunteers and conscripts
Rhodesian Light Infantry (initially all-Rhodesian, this unit became the "Foreign Legion" of the Rhodesian Army)
Mahal – non-Israeli volunteers who fought for Israel in the 1948 Arab–Israeli War. There is to this day a voluntary program called Mahal in the Israeli army.
Afghan mujahideen
Bosnian mujahideen were foreign Muslim volunteers who fought on the Bosniak side during the Bosnian War.

Current: 

Also including nationals: Tercio de Extranjeros, or Tercio, or Spanish Legion - prior to 1987 and in the 2000s, after the abandonment of conscription, the Spanish Army is again accepting foreigners from select nationalities. The Legion today accepts male and female native Spanish speakers, mostly from Central American and South American states. Recruits are required to have a valid Spanish residence permit.

Only including foreigners: French Foreign Legion - Officer corps predominantly French
International Freedom Battalion – An armed group of leftist foreign volunteers that fight in support of the Rojava Revolution in Syria.
Ukraine has requested for foreign volunteers to join the International Legion of Territorial Defense of Ukraine to help defend the country from the 2022 Russian invasion.

Units by nationality: 

American: During both world wars, American volunteers served on the allied side before the US joined the war.  During World War I, there were even a few Americans who volunteered to fly for the Imperial German Flying Corps.

The Lafayette Escadrille in the French Air Force, World War I
A number of American pilots flew with No. 32 Squadron RAF during World War I
The 7th Air Escadrille (also known as the Kościuszko Squadron) in the Polish Air Force, Polish-Soviet War
The Lincoln Brigade on the Republican side of the Spanish Civil War
The Eagle Squadrons in the Royal Air Force, World War II
The Flying Tigers in the Republic of China Air Force, World War II
Before the US entered the war, many Americans joined the Canadian Forces, especially the RCAF, and served in ordinary Canadian units.
Rachel Cox in Into the Dust and Fire records the history of five Ivy Leaguers (Chuck Bolte, Jack Brister, Bill Durkee, Heyward Cutting, and Robert Cox) who enlisted in the British Army and became the first Americans to fight the Nazis
The Crippled Eagles – American volunteers in Rhodesia (1965–1979)

Albanian: The 21st Waffen Mountain Division of the SS Skanderbeg was a division of the German Waffen-SS that was developed around a nucleus of Albanian volunteers, named after Albanian medieval lord George Kastrioti Skanderbeg. It was better known for murdering, raping, and looting in predominantly Serb areas than for participating in combat operations on behalf of the German war effort.

Bangladeshi: 8,000 young men from Bangladesh volunteered to enlist in the PLO in 1987

Belgian: Units from modern-day Belgium (then the Austrian Netherlands or United Kingdom of the Netherlands) served in the French armies of both the French Revolutionary and Napoleonic Wars
The Belgian Legion during the Franco-Mexican War of 1864-1866
The 6 Février Battalion, part of the International Brigades during the Spanish Civil War was made up of French and Belgians. Their citizenship rights were revoked as a result of their decision to serve in a foreign army.
Two Belgian units fought in the Waffen SS during the Second World War

British: During the Peninsular War, many Britons joined Spanish regular and irregular forces.
The state-sponsored Auxiliary Legion of the First Carlist War.
The British Legions in the South American Wars of Independence during the 19th century.
The British Free Corps of the Waffen SS in World War II.
2,500 British fought in the Spanish Civil War on the side of the republicans.
In the Paraguay Revolution of 1922, British pilots fought in the  Escuela de Aviación Militar.
Many Britons fought during the American Civil War for both the United States and Confederate States. 67 British soldiers in the Union Army received the Medal of Honor.
Dozens of British volunteers joined Croatian units and fought in the Yugoslav Wars between 1991 and 1995, most of them on the King Tomislav Brigade.
Hundreds of British Nationals served in the Rhodesian Security Forces during the Rhodesian Bush War in the 1970s.
A couple of dozen British volunteers joining several units of the Ukrainian military, particularly of the Ukrainian Foreign Legion, and the Azov Assault Brigade

Bulgarian: Bulgarian Volunteer Corps. Fought for the Russian Empire during the Russo-Turkish War of 1877-1878.

Bosnian: Bosnia and Herzegovina has seen some 300 people join the conflict in Syria and Iraq, making it one of the top per capita exporters of foreign fighters in Europe.
The Bosnian War attracted large numbers of foreign fighters and mercenaries from various countries. Volunteers came to fight for a variety of reasons including religious or ethnic loyalties, but mostly for money.
The 13th Waffen Mountain Division of the SS Handschar, composed mainly of Bosnian Muslims with some Catholic Croats, and mostly German officers
The 23rd Waffen Mountain Division of the SS Kama, composed of German officers and Bosnian Muslim soldiers fought in World War II on the Axis' side

Chinese: The Chinese People's Volunteer Army that fought in the Korean War was nominally composed of volunteers sent by the People's Republic of China even though it was in fact composed of regular troops of the People's Liberation Army.

Croatian: 20 to 30 Croatians fought as part of the far-right Azov volunteer battalion against Russian-backed rebels in eastern Ukraine since 2014
A total of 456 international volunteers from as many as 35 countries participated in the Croatian War of Independence (139 English, 69 French, 55 Germans, 33 Hungarians, 27 Dutch, 15 Australians)
The 369th (Croatian) Reinforced Infantry Regiment as part of German Wehrmacht, fought in World War II
The 369th (Croatian) Infantry Division, as part of German Wehrmacht, fought in World War II
The 373rd (Croatian) Infantry Division, as part of German Wehrmacht, fought in World War II
The 392nd (Croatian) Infantry Division, as part of German Wehrmacht, fought in World War II
The Croatian Air Force Legion, as part of German Luftwaffe fought in World War II on the Axis' side
The Croatian Anti-Aircraft Legion, as part of German Luftwaffe fought in World War II on the Axis' side
The Croatian Naval Legion, as part of the German Kriegsmarine, fought in World War II on the Black Sea
The Italian-Croatian Legion, unit of about 1,000 Croatian volunteers fighting for the Royal Italian Army
Four Croatian Provisional Infantry Regiments of the French Imperial Army fought in the Napoleonic Wars.
The Royal Cravat Cavalry Regiment of the French Royal Army founded in 1667 and disbanded in 1815

Czech: The Czechoslovak Legion, which fought on various fronts of WW1, as well as the Russian Civil War.
1st Czechoslovak Army Corps in the Soviet Union.

Estonian: In 1944, some 2,000 Estonians served in the Finnish Infantry Regiment 200 during the Continuation War.

Filipino: Two hundred fifty French mercenaries served with British forces that invaded Manila in 1762.  They changed sides and fought for the Spanish.
In the 1770s, the Spanish colonial army in the Philippines had an Infantry Company of Cavite Malabars
Filipinos served in the French military during the Cochinchina Campaign.
Filipinos served in the Ever Victorious Army.
The Philippine Revolutionary Army included commissioned officers who were American, Chinese, Cuban, English, Italian, Japanese, and Spanish.
The Philippine Constabulary in its early years had commissioned officers from Belgium, Cuba, England, France, Germany, Ireland, Italy, the Philippines, Poland, Puerto Rico, Scotland, Spain, Sweden, and Turkey.
Twenty-four Filipinos served in the French Army during World War I.
Some Americans served in the Philippine National Guard.
Filipinos fought on both sides of the Spanish Civil War.
During the Pacific War, Filipinos served in various pro-Japanese militias:
The Bisigbakal ñg Tagala (Tagalog "Iron Arm of Tagala") was formed in January 1945 to assist the Japanese in maintaining peace and order   in Manila.  The Bisig Bakal received weapons, uniforms, and training from the Japanese.
About five thousand Filipinos served in a militia called the Makapili, which was under Japanese command. The unit was formed on 10 November 1944 and was issued around two thousand rifles by the Japanese.  Its headquarters was located at the Christ the King compound in Quezon City.