I have 3 lights on the front of my house. One on the front porch next to the front door. The other two are next to the garage door, one on each side. They are all 3 wired together which 2 switches inside. One by the front door and the other by the door to the garage.

Here is the problem. The last light in the run started flickering. Getting dim like in the movies when a lot of power is being used somewhere else. Sometimes it will go out like the bulb is blown then later will come back on. I have noticed the next light flicker a little but nothing like the last one. The third light, the one on the porch, went out. Was out for days so I thought it was a blown bulb. Then out of the blue one day my wife turned on the lights and it worked, for one day. It has been out since, haven't checked the bulb yet.

What should I check and how? I don't want my house to burn down.

Tag.

Perhaps a bad connection somewhere in the line. Maybe moisture/corrosion in the fixture, maybe a semi-attached filament on the bulb.

If the lights are wired properly, you shouldnt get the flickering. I would try changing all 3 bulbs and see what happens. Get good bulbs- My Wife bought a pack of no-name bulbs once, and they all went bad within a week.

ETA- After re-reading your post, I'm leaning towards moisture, especially in an outside fixture.
I see it frequently in the spring and late fall, the wet, damp seasons around here.

goldcollector, sounds like you have a loose connection at one of the fixtures.turn off the circuit breaker to the circuit then remove the fixtures and check the splices at each light.

bulldog

As an former Navy electrician without any sort of certification, here's what I would suggest:

Turn off the power to the circuit at the breaker, dissasemble the offending light since it appears that this is the only component affected.  Check for loose connections.  In fact, it's probably a good idea to disconnect the wires, clean them up and reconnect them.  This is important, as a bad connection will produce heat which can burn your house down.  Re-assemble and try the system again.  

If it still won't work, secure power (navy term meaning turn off at the breaker), and check the connections at the switches.  I'm assuming that this is a two-way system where each switch turns the lights on and off.  Make sure all the connections are clean and tight again.  Try the system again.

If that don't work, the wires connecting the light to the rest of the circuit may be damaged and may have to be replaced.  Figure out where those wires connect to the rest of the system and check those connections.

Basically:

Safety first!  Always shut off the breaker before messing with wires!
Start from the problem component and check everything that could be bad.  Start with the cheap and easy and single pointfailures which could cause the problem.
Another helpful idea if you get stuck is to draw out a diagram of the system (if you can), and look for possible problems.

I hope this helps.

I have a bulb that behaves weird.   That is, it flickers and goes off randomly.   I initially thought it was the receptacle but then, after exchanging bulb I found that one is the faulty one.

I replaced it by another bulb and everything is working fine.   I then put that bulb in my closet (I'm too cheap to throw it away ) and it has been behaving erratically by not turning on some times.  Other times it turns oif by itselft...

So, based on this experience, I'd suggest you also check if the bulb itself is not the culprit.   It could be short circuiting and causing the brownouts and flickerings and high power consumption.

Proceed as above unless you discover that you have aluminum wireing. If that is the case call in a profesional and don't waste much time in doing so.
For a relatively short period of time (early 60's?) aluminum wireing was tried and it turns most any house into a fire waiting to happen . Main supply into panels and such aluminum is ok,between lights and switches it is no good. The aluminum over time corodes at the connections at switches and recepticals.This creates heat and tends to cause fires.

Outside fixtures that have upright lamp bases often fill up with bug parts. They collect around the rim between the base of the bulb and the lamp base.
When you replace the bulbs, that gunk will fall down into the base.Over time, it will collect enough to hinder proper seating of bulb.

This a bigger problem on the small lamp base fixtures.

The center of the lamp base could have lost it's tension also. If you really crank the bulb in, over time it can compress the center of the base enough to cause intermittent connection.

Bad socket.