([datetime] >= dateadd(dd, datediff(dd, 0, getdate()), 0) and
 [datetime] < dateadd(dd, datediff(dd, 0, getdate()) + 1, 0))

SET NOCOUNT ON;
USE ProofOfConcept;
GO
CREATE TABLE dbo.SARGTest (
DT DATETIME NOT NULL);
GO
CREATE CLUSTERED INDEX CID_SARGTest_DT ON dbo.SARGTest(DT);
GO
INSERT INTO dbo.SARGTest(DT)
SELECT TOP (1000000) DATEADD(DAY, CHECKSUM(NEWID())%10000, GETDATE())
FROM ProofOfConcept.dbo.Numbers AS N1
CROSS JOIN ProofOfConcept.dbo.Numbers AS N2;
GO
SELECT *
FROM dbo.SARGTest
WHERE DT >= DATEADD(DAY, DATEDIFF(DAY, 0, GETDATE()), 0)
AND DT < DATEADD(DAY, DATEDIFF(DAY, 0, GETDATE()), 1);

SELECT *
FROM dbo.SARGTest
WHERE CAST(DT AS DATE) = CAST(GETDATE() AS DATE);

DECLARE @S DATE = GETDATE(), @E DATE = DATEADD(DAY, 1, GETDATE());

SELECT *
FROM dbo.SARGTest
WHERE DT >= @S AND DT < @E;

Non-Sargable: Select ... WHERE Year(date) = 2012

WHERE 2012 = Year(date)

SET NOCOUNT ON;
USE ProofOfConcept;
GO
CREATE TABLE dbo.SARGTest (
DT DATETIME NOT NULL);
GO
CREATE CLUSTERED INDEX CID_SARGTest_DT ON dbo.SARGTest(DT);
GO
INSERT INTO dbo.SARGTest(DT)
SELECT TOP (1000000) DATEADD(DAY, CHECKSUM(NEWID())%10000, GETDATE())
FROM ProofOfConcept.dbo.Numbers AS N1
CROSS JOIN ProofOfConcept.dbo.Numbers AS N2;
GO

Also tested:

[code="sql"]DECLARE @S DATE = GETDATE(), @E DATE = DATEADD(DAY, 1, GETDATE());

SELECT *
FROM dbo.SARGTest
WHERE DT >= @S AND DT < @E;

CREATE TABLE dbo.SARGTest (
DT DATETIME NOT NULL, filler char(1) default ('a'));
GO

INSERT INTO dbo.SARGTest(DT)
SELECT TOP (1000000) DATEADD(DAY, CHECKSUM(NEWID())%10000, GETDATE())
FROM sys.objects
CROSS JOIN sys.objects as s2

CREATE  INDEX CID_SARGTest_DT ON dbo.SARGTest(DT);


DECLARE @S  datetime 
declare  @E  datetime

SET @S = GETDATE() 
SET @E = DATEADD(DAY, 1, GETDATE())

--Using the varibles cause table scan
SELECT *
FROM dbo.SARGTest
WHERE DT >= @S AND DT < @E;

--Using the same values but without the varibles use a table seek
SELECT *
FROM dbo.SARGTest
where DT > GETDATE() AND DT <  DATEADD(DAY, 1, GETDATE())
go

drop table SARGTest