What's the Binary Time?

CJam, 20 bytes

l':/60b9m<675/2bG0e[

Test suite.

Explanation

Makes use of the fact that 65536 (2¹⁶) over 86400 (the number of seconds in a day) simplifies to 512 over 675.

l     e# Read input.
':/   e# Split around ':', so we get ["hh" "mm" "ss"].
60b   e# Interpret as base-60 digits, which computes hh*60^2 + mm*60 + ss,
      e# i.e. it computes the total number of seconds. Note that this implicitly
      e# converts all three strings to integers.
9m<   e# Bitwise left-shift by 9 positions, which is the same as multiplying by
      e# 2^9 = 512.
675/  e# Divide by 675, flooring the result.
2b    e# Convert to binary.
G0e[  e# Left-pad with zeros to 16 digits.

Pyth, 31 27 bytes

.[\016.Bs*512cisMcQ\:60 675

Test suite.

Converts the input into number of seconds passed, multiply by a factor of 2^16 / 24*60*60, and then floor and convert to 16-bit binary.

Saved 4 bytes by simplifying 65536/86400 into 512/675 (stupid me).

Input/output

00:00:00    0000000000000000
11:00:00    0111010101010101
12:00:00    1000000000000000
01:30:00    0001000000000000
10:33:06    0111000010001101
09:57:30    0110101000111000
06:00:00    0100000000000000
18:00:00    1100000000000000
23:59:59    1111111111111111

TSQL(sqlserver 2012), 103 bytes

DECLARE @d datetime = '10:33:06'

DECLARE @ char(16)='',@x INT=cast(@d as real)*131072WHILE
len(@)<16SELECT @x/=2,@=concat(@x%2,@)PRINT @

Try it online

Ungolfed

DECLARE @d datetime = '10:33:06'

DECLARE @ char(16)='',
        @x INT=cast(@d as real)*131072
WHILE len(@)<16
SELECT @x/=2,@=concat(@x%2,@)
PRINT @

TSQL(sqlserver 2012), 119 106 bytes

Also included a different version without the variable @x, however it was a few bytes longer. Including the ungolfed version for those interested:

DECLARE @d datetime = '23:59:59'

DECLARE @ varchar(16) =''
WHILE LEN(@)<16
SET @+=LEFT(CAST(@d as decimal(9,9))*2*POWER(2,LEN(@))%2,1)
PRINT @