AA has remained unchanged since 1968, as already pointed out. (Good on them too, I think it looks timeless and distinctive!)
I think that except for Air France, as mentioned above, the designs of airlines like WN
have changed, especially on the fuselage. For instance, AC
has changed from an encircled, angular Maple leaf on a red tail with silver, red and white fuselage to a organic looking one on green dots.
Iberia's has been around unchanged since the 1970's, as has Alitalia's. Singapore Airlines has had a minor make-over of it's original 1970's livery, but the basic design is virtually identical to the design that took flight in 1972. While it is not unchanged, I think the variations are minor in comparison to other airline livery changes.
Other designs still around that are more than 20 years old are Qantas, Royal Jordanian, ANA and Malaysian.