Or 50's era aircraft in the 90s

This would provide the easiest example. The B-52 Stratofortress first flew in 1952 and entered service in 1955. The last one built was made in 1962. The B-52 is currently in service and scheduled to remain in service until 2045. It is a highly effective platform for delivering bombs halfway around the world, and is only employed where the risk of loss of the plane is extremely low. One could uncharitably call this plane a "bomb truck," but it is effective in that role. It has been updated over the years, but it is still in service today.

Another plane that evokes memories of the Vietnam era was outdated during its service in that conflict. The A-1 Skyraider debuted in 1945, but its rugged construction combined with its ability to go (relatively) low and slow made it a valuable ground-support aircraft. In an era of jets, SAM's, and air-to-air missiles the Skyraider (or Spad) was an anachronism--but it was also highly effective.

The most famous antiquated aircraft being effective in combat was likely the Fairey Swordfish. It was an outdated design when it entered service in 1936, sharing much more in common with its WWI brethren than its WWII counterparts. However, not only did this plane carry out the successful attack at Taranto, but it also was the plane that crippled the mighty Bismark with a torpedo strike to its rudder.

Another contender for famous outdated combat aircraft would be the Gloster Gladiator, a biplane fighter introduced in 1937. It could not compete with the monoplane fighters of its day, but it was pressed into service when war broke out. It gained a good deal of fame during its service on Malta, when these planes were used in defense. A myth was created that there were three planes, Faith, Hope, and Charity. This was overstated (the Gladiators were only alone for a short time, and other fighters did the lion's share of the work), but brave souls contesting the sky in obsolescent biplanes was a valuable story of defiance in the face of the enemy.

The success of the Po-2 is likely overstated in popular culture, but it was a somewhat effective light bomber for the Soviets against the Germans regardless of its biplane construction and massive vulnerability to foes in the air and on the ground. It was introduced in 1929 and served during WWII.

A number of nations utilized WWII aircraft for a long time after the war ended, especially smaller nations that were able to pick up surplus fighters on the cheap.

One could also point to a large number of transport aircraft, many of which have a long service life (and suffer few combat losses). Another group of candidates would come from spotter planes like the Piper Cub. It was actually fairly new during its service in WWII and it certainly doesn't look deadly, but it was devastating as a spotter plane. Its simplicity allowed it to serve from unimproved airfields near the front lines. It also served in Korea. A related plane would be the P-3 Orion, a naval patrol aircraft. It has 50 years of service (alongside the aforementioned Stratofortress, the KC-135 Stratotanker, and the C-130 Hercules) and is still in service.

I hope that gives you some answers to your question.

While this example doesn't quite make the cut in terms of the timeframes the OP specified, the outdated Fokker D.XXI:s and Brewster Buffaloes of the Finnish Air Force were very successful at the least.

It's important to note that aircraft design took leaps and bounds in the 1930s and early 1940s, and even though the Fokker for example was designed in 1935 and flew its first flight in 1936, it was already outdated by 1940. Despite that, it was put to good use during the 1939-1940 Winter War by the Finns, who used it as the main fighter. At the beginning of the war, 33 planes were operational and further 7 under repair; between them, they were credited with 151.5 victories for the loss of 10 planes and six pilots. [1]

The same could be said (but to lesser extent) about the Buffalo, which at least had folding landing gear and was considered great performer in its tests in 1938; nevertheless, reputedly the Buffalo is the only aircraft to feature in two separate books about the worst aircraft of the Second World War [2].

Not having read those books, the Finnish Air Force used it from summer 1941 to the end of 1944, achieving with it a kill ratio of 25.2:1 for the whole of the war (476 Soviet and 3 German planes vs. the loss of 19 Brewsters), and up to 67.5:1 in 1941. However, these Brewsters were better fighters than the U.S. Navy versions, as they had been lightened by the removal of (to Finns) unnecessary carrier equipment. There was even a plan to build a local copy of Brewster, the "Humu," although this did not pan out in the end. [3]

Sources

[1] Stenman and Davey (2013) Fokker D.XXI Aces of World War 2. Osprey. Kari Stenman is the best historian of Finnish Air Force and I actually refer to his Finnish works, however this is probably more accessible to non-Finns.

[2] Ford (2013). The Sorry Saga of the Brewster Buffalo: A Flying Coffin to the U.S. Marines, but a Pearl to the Finns. Warbird Books.

[3] Jukka Raustia's essay "Brewster 239 in Finnish service," http://www.warbirdforum.com/faf2con.htm