What are the implications of glibc? The library is installed on most GNU/Linux systems (and maybe others, don't know). The thing is it is supposedly licensed with LGPL, but I am not sure which version (their website, unlike other free software projects, is ambigous about it). Anyways I have am slightly worried about the implications of it. Firstly: the LGPL supposedly allows commercial projects. It places however some restrictions on the programs that use it. Since every program written in C uses standard library functions (or not every but most), then it would mean that somehow linking the program with the library makes the program bound by LGPL license. What if glibc had LGPL v3 license, at least for some files. In this case, would my program be susceptible IN ANY WAY to the restrictions against "tivoization"? I hope my understaning of this issue is wrong and LGPL does not apply to any part of my program whatsoever, even if I use standard C lib functions in my software. I would be glad for clarification of this issue, even if it seems stupid for some of you.
Under the normal circumstances that your question present (i.e. dynamic linking to a library assumed to exist on the user's system and thus not distributed with the program) the following part of the license text will save the day for any program using glibc:
A program that contains no derivative of any portion of the Library, but is designed to work with the Library by being compiled or linked with it, is called a “work that uses the Library”. Such a work, in isolation, is not a derivative work of the Library, and therefore falls outside the scope of this License.
Whatever the glibc license is, it implements, as you note, standard C lib functions. That is, it implements a standard API. Consequently, a program which uses functions from the library (without modifying the library) cannot be considered a derivative work of the library (because you could replace the library by any other implementation of the same standard API).
That being said, if you bundled the library along with your program and distributed the whole, you would still be bound by some of the terms of the license, but if you just assume the user's system has a standard C lib and dynamic link to it (as suggested by @MansGunnarsson), then you are not bound by any of these terms (whatever they may be). So the question of the license being LGPL, GPL or proprietary does not matter anymore.