It's true that the Frontier -- and the Flamingo -- are still standing on the Strip, but they're from the 1940s.
Of course, nothing remains of either original hotel-casino; the Frontier (now the New Frontier) has been torn down and rebuilt twice since it opened in 1942, and the last remnants of the '40s Flamingo were razed in the early '90s to make room for the final phase of a 20-year expansion that took the property from several hundred to more than 3,000 rooms. The Frontier has been rumored to be on the verge of implosion for years; when it finally goes, which it will, only the Flamingo will be left standing on the Strip from the '40s.
Downtown, the Golden Gate is in the original building, erected in 1906. The Las Vegas Club, in various incarnations, has been located on Fremont Street since the 1930s, but it started on the south side of the street and only moved to its current location in 1951. The original wing of the El Cortez, which stands at the corner of East Fremont and Sixth, dates back to 1941. The east side of Binion's and the Fremont remain from the '50s.
Though the garden rooms from the original Sahara are long gone, the Riviera's nine-story tower, tallest building on the Strip when it opened in April 1955, still stands.