They are yet to advance beyond the group stages, but they have still produced some memorable moments along the way, including a shock victory over European Champions West Germany in 1982.
There have also been some notable individual performances during that time, from goalkeepers to scorers of great goals.
Here, Sports Mole kicks off its countdown to the tournament in Brazil by selecting the top 10 Algerian footballers to have played the game.
10. Rachid Mekhloufi (1963-1969, 10 caps, five goals)
With Algeria not recognised by FIFA, Mekhloufi started his international career with the country of his birth's coloniser, France. Yet in 1958, the striker took a stand, left Europe and linked up with FLN, who were otherwise known as The Eleven of the Independence.
He did eventually represent Algeria, scoring five goals. Speaking about the experience of being able to sing the national anthem, the future Algeria head coach said that it "couldn't have been bought with all the gold in the world".
9. Antar Yahia (2004-2012, 53 caps, six goals)
The centre-back turned out for France at youth level, but an alteration in FIFA's rules on international eligibility allowed him to make the switch to Algeria.
He went on to become a key figure during his eight years of services to the Greens, captaining them at the World Cup in 2010 where they held England to a 0-0 draw in the group stages.
In fact, it was his goal against Egypt - one of six that he scored as a full international - that saw Algeria qualify for the tournament in South Africa.
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8. Ali Bencheikh (1976-1985, 63 caps, seven goals)
Also known as Alilou, Bencheikh was one of the star turns of the side that defeated the West Germans in 1982.
The attacker also made an impression on European clubs, with FC Nantes keen to sign him, only for the proposed transfer to be blocked by the Algerian authorities.
7. Hacene Lalmas (1963-1974, 73 caps)
Goals were Lalmas's specialty and for a long while he was the leading goalscorer in the Algerian league.
What's more, the former CR Belouizdad frontman fired in three of the five goals that Algeria scored at the 1968 African Cup of Nations.
6. Madjid Bougherra (2004-present, 60 caps, four goals)
Fans of Crewe Alexandra, Sheffield Wednesday, Charlton Athletic and Rangers will remember the 31-year-old as a solid centre-back.
Still playing and no doubt hoping to be a part of the Algeria squad this summer, Bougherra, born in France, qualifies to play for the Foxes because his grandfather was born there.
He showed his defensive qualities during the draw with England four years ago, but also has an eye for a goal, as he showed with Rangers back in 2009 when he found the net against Dundee United. It was a strike that was later voted the Goal of the Season.
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5. Djamel Menad (1982-1995, 81 caps, 25 goals)
Menad's finest moment in an Algeria shirt came during the 1990 Africa Cup of Nations when his five goals helped the hosts to win the tournament. As well as a team medal, the striker also won the Golden Boot award.
He also turned out at one World Cup, five Africa Cup of Nations events and one summer Olympic Games.
4. Salah Assad (1978-1979, 68 caps, 18 goals)
Former Barcelona and Brazil star Ronaldinho has perfected the flip-flap in recent years, but Algerians believe that Assad was the first player to have tried such a skill on the football pitch.
Such tricks earned him a move, albeit a brief one, to Paris Saint-Germain in 1983. Also, the two goals that he scored at the 1982 World Cup are still a record for his country.
3. Abdelhafid Tasfaout (1990-2002, 79 caps, 35 goals)
No player has scored more goals for Algeria than Tasfaout during his 12 years on the international scene.
Sadly for the former Auxerre and Guingamp player, his country failed to qualify for the World Cup during his stint in attack.
He suffered a serious head injury during the 2002 Africa Cup of Nations which some feared at the time would kill him, but he went on to make a full recovery.
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2. Lakhdar Belloumi (1978-1989, 101 caps, 27 goals)
A real hero among the Algerian faithful, largely because it was he that struck the winning goal against West Germany 32 years ago.
The creative midfielder won a number of awards, including being voted the African Footballer of the Year in 1981, as well as being named the fourth-best African footballer of the century.
What's more, Belloumi also holds the record for most appearances in a green shirt.
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1. Rabah Madjer (1978-1992, 87 caps, 29 goals)
You may not remember the name, but many recall the goal that he scored during the 1987 European Cup final. Playing for FC Porto, Madjer back-heeled the ball into the Bayern Munich net to set the Portuguese side on their way to a 2-1 victory.
It was a goal that went a long way to Madjer winning the African Footballer of the Year award.
Algeria will face Belgium, Russia and South Korea in this summer's World Cup, and you can follow every single match live with Sports Mole.
Continuing our 50-day countdown to the tournament, we will be looking at the greatest Argentinian players of all time tomorrow.