Is it legal to give flight instruction in my own airplane without 100 hour inspection if doing it for no charge?
I agree with acpilot that if you're merely renting the plane to this pilot then no 100hr is required. Rentals are not "for hire" operations.

I do that with a Cherokee that I rent out. I don’t provide the CFI and I do not fly it for others. Several students have taken their practical tests in the plane and I made sure they could explain the FAR to the DPE and they had no problems. 

As several commenters have stated, it gets tricky when you own the plane and provide instruction. The FAA considers lots of things as compensation that you and I would not. Goodwill, logging flight time, paying for gas, or even paying for lunch or a beer.

I found a clarification letter from the FAA at Aviation Banter.
http://www.aviationbanter.com/showthread.php?t=11563&amp;page=2

May 3, 1984
Mr. Perry Rackers
Jefferson City Flying Service

Dear Mr. Rackers
This is in reply to your request of May 1, 1984, that we render an opinion regarding the applicability
of the 100-hour inspections requirement of Section 91.169(b) of the Federal Aviation Regulations to rental aircraft.
Section 91.169(b) of the Federal Aviation Regulations provides that, except as noted in Section 91.169(c),
a person may not operate an aircraft carrying any person, other than a crewmember, for hire, and may
not give flight instruction for hire in an aircraft which that person provides unless, within the previous 100
hours of time in service, the aircraft has received either an annual or a 100-hour inspection.
If a person merely leases or rents an aircraft to another person and does not provide the pilot, that
aircraft is not required by Section 91.169(b) of the Federal Aviation Regulations to have a 100-hour i
nspection. As noted above, the 100-hour inspection is required only when the aircraft is carrying a
person for hire, or when a person is providing flight instruction for hire, in their own aircraft.
If there are any questions, please advise us.

Sincerely,
/s/
Joseph T. Brennan
Associate Regional Counsel

One correction to acpilot about the 100 hours. Once you start renting for hire, you need to do an inspection every 100 hours. The clock doesn’t restart every time you do the inspection or annual. You are allowed a little leeway to ferry the plane to the inspector, but you don’t reset the clock.
The 100-hour limitation may be exceeded by not more than 10 hours while en route to reach a place where the inspection can be done. The excess time used to reach a place where the inspection can be done must be included in computing the next 100 hours of time in service.