Since 2018, there is an easier way in Typescript, without using keyof typeof:

let obj: { [key in MyEnum]: any} =
 { [MyEnum.First]: 1, [MyEnum.Second]: 2 };

To not have to include all keys:

let obj: { [key in MyEnum]?: any} =
 { [MyEnum.First]: 1 };

To know the difference between in and keyof typeof, continue reading.

in Enum vs keyof typeof Enum

in Enum compiles to enum values and keyof typeof to enum keys.

Other differences

With keyof typeof, you cannot change the enum properties:

let obj: { [key in keyof typeof MyEnum]?: any} = { First: 1 };
obj.First = 1;
// Cannot assign to 'First' because it is a read-only property.

... unless you use -readonly:

let obj: { -readonly [key in keyof typeof MyEnum]?: any} = { First: 1 };
obj.First = 1; // works

But you can use any integer key?!:

let obj: { [key in keyof typeof MyEnum]?: any} = { First: 1 };
obj[2] = 1;

keyof typeof will compile to:

{
    [x: number]: any;
    readonly First?: any;
    readonly Second?: any;
}

Note both the [x: number] and the readonly properties. This [x: number] property doesn't exist with a string enum.

But with in Enum, you can change the object:

enum MyEnum {
    First,  // default value of this is 0
    Second, // default value of this is 1
}

let obj: { [key in  MyEnum]?: any} = { [MyEnum.First]: 1 };
obj[MyEnum.First] = 1; // can use the enum...
obj[0] = 1;            // but can also use the enum value, 
                       // as it is a numeric enum by default

It's a numeric enum. But we can't use any number:

obj[42] = 1;
// Element implicitly has an 'any' type because 
// expression of type '42' can't be used to index type '{ 0?: any; 1?: any; }'.
// Property '42' does not exist on type '{ 0?: any; 1?: any; }'.

The declaration compiles to:

{
    0?: any;
    1?: any;
}

We allow only 0 and 1, the values of the enum.

This is in line with how you would expect an enum to work, there are no surprises unlike keyof typeof.

It works with string and heterogenous enums:

enum MyEnum
{
    First = 1,
    Second = "YES"
}

let obj: { [key in  MyEnum]?: any} = { [MyEnum.First]: 1, [MyEnum.Second]: 2 };
obj[1] = 0;
obj["YES"] = 0;

Here the type is:

{
    1?: any;
    YES?: any;
}

Get immutability with readonly:

let obj: { readonly [key in MyEnum]?: any} = { 
    [MyEnum.First]: 1,
};
obj[MyEnum.First] = 2;
// Cannot assign to '1' because it is a read-only property.

... which makes these keys readonly:

{
    readonly 1?: any;
    readonly 2?: any;
}

Summary

Use in Enum if possible.

1. |undefined does not make a property optional, just means it can be undefined, there is a proposal to make |undefined members optional but currently it's not implemented. You need to use ? after ] to make all properties optional

   { [key in DialogType]?: Dialog }
   

2. You can use the dialog enum values as keys, but they need to be computed properties:

   let openDialogs: { [key in DialogType]?: Dialog } = {
       [DialogType.Options]: undefined,
   };
   

3. { [key: number or string]: Dialog } is an index signature. Index signatures are restricted to only number or string as the key type (not even a union of the two will work). So if you use an index signature you can index by any number or string (we can't restrict to only DialogType keys). The concept you are using here is called mapped types. Mapped types basically generate a new type based on a union of keys (in this case the members of DialogType enum) and a set of mapping rules. The type we created above is basically equivalent to:

   let o: { [DialogType.Help]?: Dialog; [DialogType.Options]?: Dialog; }
   

I don't think you can create enums like that, but you can have a type that is all the keys defined in an interface:

type K = keyof Interface;