First I would add the love theme from Tchaikovsky's setting of Romeo and Juliet. The whole suite is not overplayed, but that one theme is found in the Hercules cartoons and in every kind of commercial you can think of.
Also by Tchaikovsky; the Nutcracker suite. Almost every piece in this set is one most people recognize, such as the March, the Dance of the Sugar Plum Fairy, the Trépak, the Chinese and Reed-Flute dances, and the Waltz of the Flowers.
Another piece by Beethoven that's sort of iconic is the opening bars of the 8th piano sonata, the Pathétique. The whole introduction is pretty familiar to everyone. Also, the opening bars of the 5th symphony and the theme from the finale of the 9th. This last is actually the anthem of the European Union.
Of course, there's always that mighty organ prelude by Bach, the Toccata and Fugue in D Minor, BWV 565. This is, unfortuntely, permanently associated with a haunted house or some such thing in most people's minds.
Holst's planets are his only popular piece; 'Mars' is pretty overplayed.
Chopin's C Sharp minor prelude of Opus 72 is used too much , but I still love it.
A few by Grieg; the opening bars of the Piano Concerto, and the character piece 'In the Hall of the Mountain King'. Almost anyone can sing this piece, but no one can say who wrote it. Along with that last, I should mention Dukas' suite l'Aprenti Sorcier, which was greatly popularized, and subsequently degraded, by Disney's pictoral setting of it in Fantasia.
Rossini's overture to Guilliame Tell is one that few people recognize from the opening, but they say 'Hey, isn't this the theme from the Lone Ranger?' as soon as it hits the finale.
Venturing into the lesser known, I would suggest the fourteenth song from Rachmaninoff's opus 34, the Vocalize. This was set in tons of different arrangements, some by the composer himself. I don't know how many people would know it on hearing, but it is a little more popular than it should be.
Among musicians, the most overused piece is Paganini's 24th Violin Caprice in A Minor. Among those who have arranged it or written variations on it; Johannes Brahms, Franz Liszt, Sergei Rachmaninoff and Witold Lutosvafski. Even more modern versions have been produced by Benny Goodman and A.L. Webber.
Somewhat lesser known are Ravel's Boléro and his Pavane. They are both great pieces, but the former really doesn't deserve it. Even Ravel admitted that it was a sort of joke, saying that he wanted to just build one phrase and one rhythm to a singleminded climax. I immagine it is a percussionist's nightmare, as well as a conductor's. On the other hand, it has trombone glissandos.
Saint-Saens' suite, Le Carnaval des Animaux, is probably his best known and least-deserving piece. He said that it was strange that this little trifle should become so popular. He didn't even assign it an Opus number, and I believe he banned its performance during his lifetime. They're fun little character pieces though, especially ones like 'Kangaroos', 'Bones' and 'the Elephant'. 'Aquarium' and 'Cuckoo Bird Deep in the Woods' are some cool pieces also.
Of course, Saint-Saens' Danse Macabre is also pretty overrated, but still exciting.
I don't know how much this applies outside of the musical community, but I would say that Mahler's Adagietto from the 5th symphony gets a bit too much attention, overshaddowing the rest of the symphony.