Alright, these lists aren't complete, I'm sure. This is stuff off the top of my head.
Malts that are generally called 'base malts' include lightly kilned malts, cooked malts, and unmalted grains. These must be mashed as the light kilning and cooking does not convert the carbs to sugars so we must ask the enzymes to convert them for us. Here's a list of base malts.
Base Malts
Amber Malt
Aromatic Malt
Barley, Flaked
Barley, Raw
Barley, Torrefied
Brown Malt
Corn, Flaked
Melanoidin Malt
Mild Malt
Munich Malt, All Colors
Oats, Flaked
Oats, Malted
Pale Malt (2 Row)
Pale Malt (6 Row)
Pale Ale Malt (2 Row)
Pale Ale Malt (6 Row)
Peat Smoked Malt
Pilsner (2 Row)
Rice, Flaked
Rye Malt
Rye, Flaked
Smoked Malt
Special Roast
Toasted Malt
Victory Malt
Vienna Malt
Wheat Malt, All Colors
Wheat, Flaked
Wheat, Roasted
Wheat, Torrefied
Note that the darker, cooked, and unmalted malts cannot self-convert.
They do not have any or a sufficient amount of enzymes within them and thus rely on the simpler base malts (pale, pils, vienna, munich) which are commonly the biggest portion of malt bills to provide enzymes.
Adjuncts include the common crystal/caramel malts and many other common additions. The way these adjuncts are prepared at the factory has the majority of the carbs already converted to sugars. These adjuncts generally don't need mashed. They just need to be cooked to dissolve the sugars in them already created in the factory. Note however that the malted grains on this list still have some starches in them that can be converted to more sugar through a mash process.
Adjuncts
Biscuit Malt
Black Barley/Patent Malt
Brown Sugars
Candi Sugars
Cane (Beet) Sugar
Cara-Pils/Dextrine
Caraamber
Carabrown
Carafoam
Caramel/Crystal Malt, All Colors
Caramunich Malt, All Colors
Carared
Cararye
Caravienne
...heck, all of the 'Cara's...
Chocolate Malt, All Colors
Corn Syrup
Grits
Honey
Invert Sugar
Maple Syrup
Milk Sugar (Lactose) (not fermentable but doesn't need mashed)
Molasses
Roasted Barley
Special B Malt
Sugar, Corn (Dextrose)
Sugar, Dememera
Sugar, Table (Sucrose)
Sugar, Turbinado
Fermentability is another story. Generally, the base malts are the most fermentable, besides the simple sugars which are nearly 100% fermentable. The rest are less so. There's no rule or hard/fast numbers to give you to say that Carapils is 50% fermentable, etc. The best idea to keep in your head as you start formulating your own recipes is that when your base malt (or base malts, if you're using multiple in a recipe, like pale malt and flaked barley and wheat) gets to be less than 85% of the recipe, you should take another hard look at the recipe you're formulating. If you're working on a light, simple beer, I'd take a hard look at the recipe if my base malts got to be less than 90% of the malt bill.