Are they liquids or explosives or weapons of some sort? That's the stuff TSA is supposed to be looking for.
Consult the TSA website for the authoritative list of prohibited items:
http://www.tsa.dhs.gov/travelers/airtravel/prohibited/permitted-prohibited-items.shtm

Candles are generally parafin, a highly flammable gel and will not be allowed into an aircraft cabin.

I say it's OK - just don't light the candles

My cotton clothes are highly flammable yet I wear them on planes all the time. I've carried candles in carryon bags before without a problem.

If no-parrafin is a new (or old) TSA rule Jeff, please post a link with that info so we can all learn.

Recently I had a candle on a flight and the TSA agent said we could not keep it. When we questioned the rule he kindly asked for the supervisor who allowed the candle. (They were all very kind.)

Jeff - wrong.

Per TSA regs - "gel-type" candles are not permitted in carry-on luggage. What constitutes a "gel-type" candle is up to interpretation by the TSA agent who screens your bag. The difficulty is when the screener says "NO" you generally don't have much recourse.

I don't understand what a "gel-type" candle is?

But I've brought the regular kind in my carry-on many times (great souveniers from Mexico or Hawaii). They have never been questioned.

gel type candles are just that - rather than being made of solid wax they are a gel (sort of like Sterno in consistency.) Because they are a gel they must be in some sort of container as they would otherwise not hold shape and ooze all over the place.

I cannot imagine that even a TSA agent would mistake a solid candle for gel. I have carried a candle in my carry-on bag as recently as two weeks ago without problem.

I stand corrected.