Free Transport

Legs
Walking is free and healthy. In Energy and Equity Ivan Illich noted that walking is about the same net speed as travelling in automobiles - if the time needed to earn the money to buy and run the car and road system are taken into account (even disregarding the effects of accidents!) the effective speed of car users is no faster than walking.

Bicycling
Ivan Illich recommended bike riding as a sweet spot of speed and expense, and of course it is also healthy. Charities such as http://Re-cycle.org are committed to providing free bicycles to those who can beenfit from them. See this list of bicycle sharing systems from Wikipedia.

Motorised Transport
Most motorised vehicles have many free seats for most of the time. Some drivers are thoughtful enough to let strangers travel with them, either on an ad hoc basis (see HitchWiki.org), or by use of systems such as the below websites, which match drivers to passengers:

Some people offer motorised transport on a 'give what you can' basis: