Where do the constants for SHA-1/2/3 come from? My request is:
I need to know the source of constants (shift constants, IV, or S-Box) for the following algorithms:  


SHA-1  
SHA-2 (all sizes)  
SHA-3  


Examples:  


BLOWFISH uses the hexadecimal values of PI. 
SKEIN uses chosen constants from the output of running RJINDAEL in CTR mode on all zeros nonce and all zeros key and counter starting from 0 to one million.  
CHACHA uses statements "expand 32-byte k" and "expand 16-byte k".
Regarding the IVs and round constants of hash functions...

The question for SHA1 and SHA2 families have already been answered. Rotational constants were chosen by the designers to make the hash functions secure (or in the case of SHA1, not secure enough). Derivative hash functions such as SHA-224 and SHA-384 use different initial values which are simply the next primes on the list (9 through 16th). SHA-512/t uses different initial values based on the output of a slightly modified version of SHA-512 processing a short string.

SHA3 is a completely different construction. It has no initial values, the working state is simply all 0 bits. The round constants of SHA3 and Keccak are based on a linear feedback shift register, this takes up much less space in code vs hard coded numbers like those in SHA-2, and very cheap to implement in hardware. The rotational offsets for SHA3 and Keccak are a reordered set of triangular numbers modulo the lane size, which for SHA3 is 64-bits. This is also very cheap in both software and hardware, as it is simply a reordering of bits within the state.