In 1953, a company called Risdon Beasley Ltd, which is/was one of the world's leading deep sea salvage companies, tried to find the wreck by setting off explosives underwater (!) and using a sonar to record the echo profiles.
In 1980, Jack Grimm (a Texas millionaire who made world headlines by searching for Noah's Ark and Bigfoot) headed an expedition which used sonar. Bad weather hampered the search (isn't that always the case). He returned in 1981 and again in 1983 but returned empty-handed all three times. He did, however, publish a photo that he claimed to be one of the propellers lying on the seabed.
I've seen the photo (although for some reason no one else has or SOMEONE would have it online on one of the 8 million Titanic sites around). It could be anything and I think that Mr. Grimm was reaching. Didn't he die a couple of years ago?
As far as there being other shipwrecks...there ARE other shipwrecks but there are things about those 10 days that have all stacked up to give the whole affair a mystique:
1) A boatload of rich and famous people (think of Donald Trump, Rudy Gulliani, Brittney Spears, Bill Gates, Leona Helmsley, General Wesley Clark, and Martha Stewart all taking a pleasure cruise together).
2) A new ship that is the top of the line...largest in the world (think of all of the above people on the first voyage of a new type of ship that has any amenity you can think of).
3) This brand new ship that is extremely expensive and stuffed full of high-wattage celebs sinks killing almost all of them.
There are just too many factors that make it an event that will attract people.
Whether you hated the movie or just hate shipwrecks (who wants to dive two miles underwater to look at someone's castoffs), you have to admit that there is just too much about the disaster that warrants movies and books written about it.
I'll admit that there are many shipwrecks that are more fascinating. Empress of Ireland, Andrea Doria, Lusitania. But the Titanic has factors the others don't have...they don't all have the same scope. Empress of Ireland had the loss of life. Andrea Doria was one of the most luxurious of the day. Lusitania had celebs. But they didn't have all of it.