Linux distros can come in varying sizes ranging from a few MBs to several GBs. And many of them come with a whole set of packages that may not be necessary for all needs. For example, if you want a server you may not need the media players or associated codecs in it. The good new is that Linux can be customized to an extreme degree to fit your needs and some of the distros give you the flexibility to choose packages and cook your own Linux distro without much effort. You can then try it out on a virtual machine before installing on hardware and see if it suits your needs.
- SuSE Studio: I think this is the highest degree of customization that any distro supports officially. You can build your own distro from the scratch.
- Porteus: A bleeding edge mini distro. You can choose many of the components.
- Ubuntu Mini Remix: A 200MB minimal Ubuntu distro that comes with customization tools in it. You can remaster your own Ubuntu variant from there.
- Ubuntu Builder: This is a utility that can create custom ISOs from base Ubuntu (or any Ubuntu variant like Mint) ISOs. Works even with Ubuntu Mini Remix.
- Novo Builder: A bunch of scripts for generating Debian based distros (including Ubuntu).