This obviously has morphed from what I thought was a request for what some folks though of as "classic" sandwiches, into what everyone's "favorite" sandwiches are. Let's face it guys, many of the sandwiches listed here aren't well-known "classics" by any stretch of the imagination.
That said, for me, my favorite "classic" sandwiches would be:
Reuben - "real" corned beef, swiss cheese, sauerkraut, & Thousand Island dressing on seeded rye bread - grilled.
Traditional "Club Sandwich" - a variety of meats (always bacon as one) & cheeses, with lettuce & tomato stacked between 3 slices of toasted bread.
BLT - Bacon, lettuce, & tomato with mayo on toasted bread.
Tuna Salad/Egg Salad/Ham Salad/Chicken Salad - self-explanatory.
Po' Boys - Fried oyster, shrimp, or fish on tartar-sauce spreaded toasted baguettes.
There are, of course, many more "classics", but those are my favorites.
As far as "my" personal favorite sandwiches, apart from the above:
"Rachel" - same as the traditional "Reuben", but subbing in smoked turkey for the corned beef, & cole slaw for the sauerkraut. Very popular down here in the South. Didn't think I'd like it at first, but am now a fan.
Mashed sardines with sliced red onion & lettuce.
Limburger or Liederkranz cheese (which is now back on the market) with sliced sweet onion.
Roast beef with swiss cheese on white with mayo.
Turkey with swiss cheese on white with mayo.
Brie & smoked turkey with sun-dried tomatoes & lettuce on a crusty roll.
Fried or sauteed soft-shell crab with tartar or remoulade sauce & lettuce on a crusty roll.
Gee - I could really go on forever. Sandwich combinations are one of those "infinity" items.