Is it possible to pull only a part of a git repository?

[Micha Feigin]

I have a growing number of projects that I'm trying to manage in my git
repository. Currently they are all in the same repository to make it easier to
sync it with the server (for backups / synchronization with other machines). 

Now, I want to be able to work on only one project at a time, or give people
access to only part of the repository. Another options is to split up the
repository into several repositories once things grow too big.

Is this possible with git, i.e cloning on part of the repository? If not, is it
possible with other version control mechanisms (I think that svn was able to do
that if memory servers). 

For example, I want to do a "git clone repo/dir" instead of "git clone repo"

Also, any suggestions for some good git tutorials. I know all the bases, but I
want some good tutorial and reference for poweruser things, like proper use of
branches, tags, subtrees, merging etc.

Thanks