Here is something that should get you what you want.
--First i just created some test data
if object_id('tempdb..#temp') is not null drop table #temp
select '8/15/1995' as DOB into #temp union all --Note this person is 21
select '8/16/1995' union all --Note this person is 21 TODAY
select '8/17/1995' union all --Note this person is 21 TOMORROW
select '4/11/1996' union all
select '5/15/1997' union all
select '9/7/2001'
--set the years old you want to use here. Create another variable if you need to use ranges
declare @yearsOld int
set @yearsOld = 21
select
convert(date,DOB) as DOB,
--This figures out how old they are by seeing if they have had a birthday
--this year and calculating accordingly. It is what is used in the filter
--I only put it here so you can see the results
CASE
WHEN CONVERT(DATE, CONVERT(VARCHAR(4), YEAR(GetDate()))+ '-'+ CONVERT(VARCHAR(2),MONTH(DOB)) + '-' + CONVERT(VARCHAR(2),DAY(DOB))) <= GETDATE() THEN DATEDIFF(yy,DOB,GETDATE())
ELSE DATEDIFF(yy,DOB,GETDATE()) -1
END AS YearsOld
from #temp
where
--here is your filter. Feel free to change the >= to what ever you want, or combine it to make it a range.
CASE
WHEN CONVERT(DATE, CONVERT(VARCHAR(4), YEAR(GetDate()))+ '-'+ CONVERT(VARCHAR(2),MONTH(DOB)) + '-' + CONVERT(VARCHAR(2),DAY(DOB))) <= GETDATE() THEN DATEDIFF(yy,DOB,GETDATE())
ELSE DATEDIFF(yy,DOB,GETDATE()) -1
END >= @yearsOld
EDIT
This is your method which doesn't account for if they have had a birthday this year. I use some test data. Notice the person born on 8/18/1995. They turn 21 tomorrow but using (DATEDIFF(hour,DOB,GETDATE())/8766) >= @yearsOld includes them when it shouldn't...
--First i just created some test data
if object_id('tempdb..#temp') is not null drop table #temp
select '8/15/1995' as DOB into #temp union all --Note this person is 21
select '8/16/1995' union all --Note this person is 21 TODAY
select '8/18/1995' union all --Note this person is 21 TOMORROW
select '4/11/1996' union all
select '5/15/1997' union all
select '9/7/2001'
--set the years old you want to use here. Create another variable if you need to use ranges
declare @yearsOld int
set @yearsOld = 21
select
convert(date,DOB) as DOB,
--This figures out how old they are by seeing if they have had a birthday
--this year and calculating accordingly. It is what is used in the filter
--I only put it here so you can see the results
CASE
WHEN CONVERT(DATE, CONVERT(VARCHAR(4), YEAR(GetDate()))+ '-'+ CONVERT(VARCHAR(2),MONTH(DOB)) + '-' + CONVERT(VARCHAR(2),DAY(DOB))) <= GETDATE() THEN DATEDIFF(yy,DOB,GETDATE())
ELSE DATEDIFF(yy,DOB,GETDATE()) -1
END AS YearsOld
from #temp
where
--here is your filter. Feel free to change the >= to what ever you want, or combine it to make it a range.
(DATEDIFF(hour,DOB,GETDATE())/8766) >= @yearsOld
RESULTS
DOB | YearsOld
1995-08-15 | 21
1995-08-16 | 21
1995-08-18 | 20 --this shouldn't be here...