The most simple and straightforward C/C++ implementation that I found is in a link at the bottom of this page:
Web Page: http://www.barrgroup.com/Embedded-Systems/How-To/CRC-Calculation-C-Code
Code Download Link: https://barrgroup.com/code/crc.zip
It is a simple standalone implementation with one .h and one .c file.
There is support for CRC32, CRC16 and CRC_CCITT thru the use of a define. Also, the code lets the user change parameter settings like the CRC polynomial, initial/final XOR value, and reflection options if you so desire.
The license is not explicitly defined ala LGPL or similar. However the site does say that they are placing the code in the public domain for any use. The actual code files also say this.
Hope it helps!