According to The Phrase Finder, the phrase the grass is always greener on the other side of the fence:

expresses the idea that other people’s situations always seem better than one’s own. The proverb carries an implied warning that, in reality, the grass is equally green on one’s own side and that you should be satisfied with what you have.

It’s earliest known appearance in print was apparently on 24th February 1917 in the Kansas Farmer – The Farm Paper of Kansas:

A song written in 1924 by Raymond B. Egan and Richard A. Whiting was titled The Grass is Alway Greener (In The Other Fellow’s Yard).

Other versions of the phrase appeared before then. For example, in The New York Times in June 1853:

It bewitched your correspondent with a desire to see greener grass and set foot on fresher fields.

However, according the English Language & Usage, the ideas expressed by the phrase are a lot older than that. For example, in Ovid’s poem Ars Amatoria (The Art of Love) Book I Part IX, which was written in 2 AD, he says:

Fertilior seges est alienis semper in agris,
Vicinumque pecus grandius uber habet.

Translations of this include:

• The crop of corn is always more fertile in the fields of other people;
  and the herds of our neighbours have their udders more distended. [source]
• The seed’s often more fertile in foreign fields,
  and a neighbour’s herd always has richer milk. [source]
• A larger crop adorns our neighbour’s field,
  More milk his kine from swelling udders yield. [source]

Here are versions of the expression in other languages [source].

French:

• l’herbe est plus verte ailleurs
  the grass is greener elsewhere
• l’herbe est (toujours) plus verte de l’autre côté de la montagne
  the grass is (always) greener on the other side of the mountain
• l’herbe est toujours plus verte dans le pré du voisin
  the grass is always greener in a neighbour’s field
• l’herbe est toujours plus verte chez le voisin
  the grass is always greener at the neighbour’s

Spanish:

• el pasto siempre es más verde del otro lado
  the grass is always greener on the other side
• la hierba parece más verde al otro lado de la valla
  the grass looks greener on the other side of the fence
• la gallina de mi vecina más huevos pone que la mía
  my neighbor’s hen lays more eggs than mine
• la gallina de mi vecina siempre es más gorda que la mía
  my neighbor’s hen is always fatter than mine

Portuguese:

• a grama é sempre mais verde do outro lado
  the grass is always greener on the other side
• a galinha da minha vizinha põe mais ovos que a minha
  my neighbor’s chicken lays more eggs than mine
• a cabra da minha vizinha dá mais leite que a minha
  my neighbor’s goat gives more milk than mine

Welsh:

• mae’r glaswellt yn lasach ar yr ochr arall bob tro
  the grass is always greener on the other side
• man gwyn man draw
  white spot over there

Irish:

• Is glas iad na cnoic i bhfad uainn
  The far away hills are green
• Is milse gcónaí arian na gcomharsan
  The neighbour’s money is always sweet

Scottish Gaelic:

• ‘S e miann na lacha an loch air nach bi i
  The duck prefers the loch where it isn’t

Korean:

• 남의 떡이 더 커 보인다 (nam-ui tteog-i deo keo boinda)
  someone else’s cake looks bigger

Are there interesting equivalents of this phrase in other languages?

Here’s a song I wrote in October 2023 called ‘The Other Side’ based on this saying: