Alsa (the modules), along with the kernel is one of those things which you should avoid to upgrade. It's usually recomended to make a custom kernel and stick with that.
The Alsa libs/tools should also be kept the same that what your kernel is using. That means that, unless you do upgrade your Kernel to the one in current, and the alsa modules, you'd have to upgrade alsa from source.
The ways to deal with this is:
If you want to use Slackware's
Do download the -current Kernel package (and its modules package) and alsa modules, libs, utils.
Do a manual install of the Kernel (move the image to /boot, edit /etc/lilo.conf, run lilo) install the kernel modules and the alsa modules
Restart the system and run the new kernel, to make sure it'll work on your system.
Do install the alsa libs, and utils.
If you want to use a custom kernel (which is recomended anyway):
You Could download the kernel-source package instead (or download the lastest from www.kernel.org
You Should then configure the kernel, make the kernel and modules, and install the kernel. If it's a 2.6.x you Could enable Alsa from there and forget the Alsa-modules packages.
If you're using the kernel-source package, you could then install Alsa related stuff, otherwize you either compiled alsa with the kernel or go to www.alsa-project.com
and download all of Alsa and compile it by your self (make sure to remove the packages before).
Both metods usually work (I've done them, both). The last one is IMO better, because you use a custom compiled kernel, and you could enable the alsa within the kernel and forget about keeping the alsa-modules package (which may end up breaking stuff).
Also, the lastest -current, because of changes to udev and hotplug, runs better using a 2.6.16.x kernel (or a 2.4.x).