Is there a comprehensive list of functions with operator forms?

Edit: version 11.0 update. Now it is superset of TypeSystem`$OperatorForms. It now also includes operator forms that have different names than the functions they're currying, like EqualTo.

One can find these functions in the documentation by keywords "operator form"

Select[Names@"*", StringMatchQ[ToString@ToExpression[# <> "::usage"], 
    "*operator form*"] &]

{"AllTrue", "AnyTrue", "Append", "Apply", "AssociationMap", \
"Between", "Cases", "CellularAutomaton", "ContainsAll", \
"ContainsAny", "ContainsExactly", "ContainsNone", "ContainsOnly", \
"Count", "CountDistinctBy", "CountsBy", "DatabinAdd", "Delete", \
"DeleteCases", "DeleteDuplicatesBy", "EqualTo", "Extract", \
"FeatureDistance", "FirstCase", "FirstPosition", "Fold", "FreeQ", \
"GreaterEqualThan", "GreaterThan", "GroupBy", "Insert", "KeyDrop", \
"KeyExistsQ", "KeyFreeQ", "KeyMap", "KeyMemberQ", "KeySelect", \
"KeySortBy", "KeyTake", "KeyValueMap", "LessEqualThan", "LessThan", \
"Lookup", "Map", "MapAt", "MapIndexed", "MatchQ", "MaximalBy", \
"MemberQ", "Merge", "MinimalBy", "NoneTrue", "Position", "Prepend", \
"Replace", "ReplaceAll", "ReplacePart", "Scan", "Select", \
"SelectFirst", "SortBy", "StringCases", "StringContainsQ", \
"StringDelete", "StringEndsQ", "StringFreeQ", "StringMatchQ", \
"StringPosition", "StringReplace", "StringReplacePart", \
"StringStartsQ", "SubstitutionSystem", "TakeLargest", \
"TakeLargestBy", "TakeSmallest", "TakeSmallestBy", "UnequalTo"}

Unfortunately, this list is missing at least AlphabeticOrder, FoldList and TuringMachine.

There is a global variable that purports to contain a list of operator forms, TypeSystem`$OperatorForms. I say "purports", because the list is missing some of the forms found by @ybeltukov's method. But to its credit, it correctly identifies the operator form of ReplaceAll which is mentioned in neither a usage message nor the documentation, and also correctly omits StringCases which has no operator form despite the usage message claiming otherwise:

Needs["TypeSystem`"]

$typeSystem = SymbolName /@ TypeSystem`$OperatorForms;

$usages =
  Select[
    Names@"*"
  , StringMatchQ[ToString@ToExpression[#<>"::usage"],"*an operator form of*"]&
  ];

$usages ~Complement~ $typeSystem
(* {AssociationMap,CountDistinctBy,DeleteDuplicatesBy,MapAt,Merge,StringCases} *)

$typeSystem ~Complement~ $usages
(* {ReplaceAll} *)

There are three other operators which exhaustively partition TypeSystem`$OperatorForms into the categories "left", "right" and "3-2":

TypeSystem`$LeftOperatorForms

(* {Map,KeyMap,Apply,Scan,MapIndexed} *)

TypeSystem`$RightOperatorForms

(* {Prepend,Append,GroupBy,CountsBy,Count,Position,FirstPosition,SortBy,KeySelect,
    Select,SelectFirst,Delete,Extract,Replace,ReplacePart,ReplaceAll,Cases,
    DeleteCases,FirstCase,AnyTrue,AllTrue,NoneTrue,KeyExistsQ,KeySortBy,
    KeyTake,KeyDrop,MaximalBy,MinimalBy,MatchQ,FreeQ,MemberQ} *)

TypeSystem`$ThreeTwoOperatorForms

(* {Insert} *)

These categories appear to identify the position(s) of the curried arguments.

The results shown here are from version 10.0.1.

From version 10.3 you can use WolframLanguageData.

WolframLanguageData[EntityClass["WolframLanguageSymbol", "Curryable"]]

As of 11.0, this appears to be the most reliable solution:

Unfortunately, this method is not perfect either: at least TuringMachine is missing from it.

Hope this helps.