Add a column with a default value to an existing table in SQL Server

ALTER TABLE <table name> 
ADD <new column name> <data type> NOT NULL
GO
ALTER TABLE <table name> 
ADD CONSTRAINT <constraint name> DEFAULT <default value> FOR <new column name>
GO

When adding a nullable column, WITH VALUES will ensure that the specific DEFAULT value is applied to existing rows:

ALTER TABLE table
ADD column BIT     -- Demonstration with NULL-able column added
CONSTRAINT Constraint_name DEFAULT 0 WITH VALUES

Syntax:

ALTER TABLE {TABLENAME} 
ADD {COLUMNNAME} {TYPE} {NULL|NOT NULL} 
CONSTRAINT {CONSTRAINT_NAME} DEFAULT {DEFAULT_VALUE}
WITH VALUES

Example:

ALTER TABLE SomeTable
        ADD SomeCol Bit NULL --Or NOT NULL.
 CONSTRAINT D_SomeTable_SomeCol --When Omitted a Default-Constraint Name is autogenerated.
    DEFAULT (0)--Optional Default-Constraint.
WITH VALUES --Add if Column is Nullable and you want the Default Value for Existing Records.

Notes:

Optional Constraint Name:
If you leave out CONSTRAINT D_SomeTable_SomeCol then SQL Server will autogenerate
    a Default-Contraint with a funny Name like: DF__SomeTa__SomeC__4FB7FEF6

Optional With-Values Statement:
The WITH VALUES is only needed when your Column is Nullable
    and you want the Default Value used for Existing Records.
If your Column is NOT NULL, then it will automatically use the Default Value
    for all Existing Records, whether you specify WITH VALUES or not.

How Inserts work with a Default-Constraint:
If you insert a Record into SomeTable and do not Specify SomeCol's value, then it will Default to 0.
If you insert a Record and Specify SomeCol's value as NULL (and your column allows nulls),
    then the Default-Constraint will not be used and NULL will be inserted as the Value.

Notes were based on everyone's great feedback below.
Special Thanks to:
    @Yatrix, @WalterStabosz, @YahooSerious, and @StackMan for their Comments.

ALTER TABLE Protocols
ADD ProtocolTypeID int NOT NULL DEFAULT(1)
GO

The inclusion of the DEFAULT fills the column in existing rows with the default value, so the NOT NULL constraint is not violated.