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When Botafogo chose their black and white stripes in 1904 they did so on the insistence of one of their founder members who had just returned from college in Italy. This fellow, Itamar Tavares, was an admirer of Juventus.
In 1904 Juventus had adopted these colours accidentally. Abandoning their original pink jerseys they had intended to take the colours of Nottingham Forest. However, they inadvertently ended up with the colours of the other Nottingham team, Notts County.  
Notts County had been playing in black and white stripes since 1890.

Tottenham Hotspur's white strip is a classic. However, they played in a variety of colours before taking to the white in homage to Preston North End in 1898. Preston had first used these colours  in 1888. Amongst Tottenham's earlier kits (1885-1887) was a copy of  Blackburn Rovers' famous blue and white 'quarters' (first worn by Rovers in 1882). 
Another team to pay their respects to Blackburn by imitating their colours was Morozovtsi Orekhovo-Zuevo Moskva, formed in 1887 by English mill owners Clement and Harry Charnock. This club were the forerunners of Dinamo Moscow.

Nottingham Forest had worn redcurrant shirts since their earliest days (1868). In 1886 2 former Forest players who had joined the newly formed Dial Square approached their old club for assistance and were given a set of kit. Dial Square became Woolwich Arsenal in 1893.
  In 1906, on a visit to England Dr. Petřík, president of Sparta Prague, acquired a set of jerseys in Woolwich Arsenal's  redcurrant.

In 1904 Nottingham Forest changed from redcurrant to scarlet. When Forest toured south America in 1905 Arístides Langone, the President of the Argentinian club Independiente (Avellaneda) , was inspired to change his team's colours from blue and white halves to red.

The famous English amateur club Corinthians played in white shirts and blue knickers very similar to the England national team (Corinth were formed in 1882 in  an effort to bring the England team up to the level of Scotland).
In 1902 a rift in the Español de Madrid club led to the formation of Madrid Football Club (later Real Madrid). Madrid were coached by an Englishman, Arthur Johnson, and this influenced their adoption of the white strip of the world famous English club.
 Sport Club Corinthians Paulista took both the name and  the colours (although their jerseys were originally cream rather than white) of the 1910 English tourists who inspired their foundation.

Burnley played in a wide  variety of colours during the first 18 years of their existence. Then, from 1900 to 1909 they played in green. This brought them no luck, so they adopted the claret and blue of Aston Villa.

In his youth Joan Gamper (then known as  Hans Kamper) played for FC Basel in his native Switzerland. The club colours were garnet and blue. When Gamper founded Barcelona  in 1899 they adopted these colours.

From 1902 Athletic Bilbao and Club Bizcaya  played in a strip resembling that of Blackburn Rovers. In 1909 Athletic asked Juan Elorduy, a student who was travelling to London,  to buy them a new set of kit. Not being able to acquire the chosen colours, Elorduy settled for the red and white of  Southampton* as these were also the civic colours of Bilbao. Bilbao's sister club, Athletic Club de Madrid, founded by Basques in the capital, were given half of the kit, and retain the colours in their present incarnation as Atlético Madrid.

* Wikipedia incorrectly gives Sunderland.  Why would a journey from London to Bilbao include a stop in Sunderland ?

In 1899 Sparta Rotterdam decided to adopt the colours of Sunderland. Sunderland had introduced the red and white stripes in 1887, adding the black knickers in 1888.

Formed in 1885 Millwall Rovers were a works side, based at JT Morton's cannery and food processing plant on the Isle of Dogs. Morton's was a Scottish firm and many of the employees/ players were Scots. They chose, therefore, the colours of the Scotland national side for their strip.

Italy- The Azzuri- began by playing international games in a white strip, copied from that of the dominant team of the era, Pro Vercelli. Italy changed to blue after one year (in 1911), generally keeping the white as a change strip. 

Founded in  1905 as Club Atlético Estudiantes, Club Estudiantes de La Plata took the colours of Alumni Athletic Club, the most successful team in the early days of football in Argentina.