I just uncommented a current mirror and noticed in the process of updating that a lot of new packages had been included that take care of basic system functionality, core-utils, a new gcc, new kernel (which i did not select to install) and modules etc.
One of the first things i did after installing was compile a new kernel with the sources from kernel.org, version 3.4.0. It was on another partition and already configured for my hardware.
So my question is, with the updates in core system stuff, would it be a good idea to recompile and reinstall my current kernel, or is that not necessary?

I would recompile and reinstall, as main libraries have been upgraded since Slackware-13.37

The safest way IMHO is to re-use a config file in /boot as .config, "make oldconfig" then adapt as needed with "make <some_option>config".

At least that's how I do it

I must admit I don't need a lot of customization for my hardware so I wouldn't mind so much to loose previous tweaking.

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There's no need to rebuild the kernel just because of the current updates, but as 3.4.1 is out with a good heap of fixes it's not a bad idea to build yourself a new one anyway.

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I think im going to take both suggestions and "make oldconfig" on the 3.4.1 kernel with my .config from 3.4.0