The carbon carbon bond (C-C for short) is probably one of the simplest functional groups.  A functional group is a group of atoms (or sometimes just one atom) that have a characteristic chemical property. 

We have already seen that a C-C single bond is formed with sp³ hybridisation.  The name of the group of molecules that contain only C-C single bonds and C-H bonds is the alkanes.

Alkanes can rotate freely about a single C-C bond.

One important property of carbon is that the overlap of an sp³ orbital with another carbon is not limited to one per atom, but can be 2,3 or even 4.  This means that we can form carbon chains:

And these chains can be branched e.g.:

Depending on the number of carbon atoms it is attached to, a carbon is called primary (1), secondary (2), tertiary (3) or quaternary (4).

It is useful to know some of the names of these compounds:

Formula	Name
CH4	Methane
C2H6	Ethane
C3H8	Propane
C4H10	Butane
C5H12	Pentane
C6H14	Hexane

There are also some useful abbreviations of groups of atoms (parts of a molecule - not a complete molecule) commonly encountered (the wavy line represent where the group is joined to the rest of the molecule):

Structure	Name
	Propyl
	Isopropyl
	Butyl
	sec-Butyl
	Isobutyl
	tert-Butyl

Properties:

Alkanes are actually very inert.  Despite their tendency to burn (all the alkanes up to octane are highly flammable, and many beyond octane burn readily), which gives the impression that they are reactive, they don't react with much else. 

One of the few things they do react with is radicals.  A radical is a species with an unpaired electron, and is highly reactive.  They are denoted by drawing a dot (^.) next to them to represent the unpaired electron.  An example of a simple radical is a chlorine atom (i.e. Cl, not Cl₂).  The formation of Cl^. from Cl₂ can be achieved with ultraviolet light.  If this is done in the presence of an alkane, then a chain reaction occurs (there will be more detail on radical reactions, in the radical section):

etc.

As you can see, the reaction systematically substitutes one Cl atom for each H atom, so (assuming there is enough chlorine) we will end up with CCl₄.