Many moons ago I wrote an app (for the Amiga!) which was like a Swiss army knife for guitar players, showing chords and scales and identifying chords you threw at it and such like. This chord identifying function gave me hours of fun because not only did it show you exact matches for the notes you clicked on the fretboard (with all inversions), but it also told you all the chords that those notes were contained within too. So if you clicked the notes of a C major chord it would tell you that those notes were contained within Am7, D11, Fma9 etc. It was a great source of inspiration when writing songs. There was also a function by which you could indicate a chord and it would give you a selection of "next chords" that this chord could progress too, including chords in other keys. It was a great tool for coming up with interesting and surprising changes. I wish I still had my Amiga :(
 
I think I've talked about this before but one wacky technique I use to come up with chords and melodies is to take a loop, which could be anything from a full band playing to an orchestra or small ensemble (or just me playing guitar through loads of crazy effects), then let Melodyne's polyphonic note detection do its thing in turning it into MIDI. I then play that MIDI through a synth and because Melodyne is picking up all sorts of insane overtones and getting confused one way or another with complex polyphonic material, the result is usually a chaotic train wreck. But I find that by slowly chipping away at the MIDI chaos in the piano roll - removing notes that obviously don't fit, moving other notes around and even adding some of my own - I can slowly evolve something that makes musical sense and is completely different to anything I would have come up with through noodling on my own. 

Here's a quick example of the kind of wackiness I come up with using the Melodyne technique described above. It still needs a lot of work (especially with the velocities, which are often all over the place after a Melodyne conversion). This is just output to a quick patch I made with Rounds. Pretty crazy huh? You end up with some very odd rhythms as well. This was just some crazy MIDI I had lying around from a Melodyne conversion from god knows where...I can't even remember. I think it was me playing guitar through loads of delays and stuff. I have loads of raw MIDI material lying around like this that I convert and then set aside, recently I picked this one and chipped away at it and sculpted something which kind of makes Melodic sense in a wacky sort of Zappa-esque kind of way....maybe not your cup of tea, but the point is that this is something I would have never come up with using conventional writing techniques....
 
https://soundcloud.com/sharke-1/record-6-2459

The most important technique I have ever learned was
 
Press the Record Button.
When it comes to recording I have paraphrased Amalric's quote about war, "Kill them all and let God sort it out."  I say "press record and let God sort it out."
 
 
Jesse Q. Screed

My iPhone voice memo recorder is full of me singing bits of lyrics, little melodies and stuff that pop into my head.  I sort through that every once in a while and find the good nuggets.

My songs usually begin as paranoid ideation, where I assign false motives to others.  But I won't bore you with the details!

The only technique that seems to work for me is to keep plugging away at it until I feel it's done.

I think that the other posters have provided some very good ideas.  I notice that there is a lot of free form inspiration going on, letting the muse find you.  I have learned a lot by reading this topic.  The way you write a song says a lot about your personality.  Thanks to all those who posted such great ideas.
 

sven450
My iPhone voice memo recorder is full of me singing bits of lyrics, little melodies and stuff that pop into my head.  I sort through that every once in a while and find the good nuggets.

This is a good idea.  I have a handheld Olympus voice recorder that I do the same thing with.  Sometimes, when I wake up before the sunrise, and I go for a walk, some very interesting things can pop into your mind.  I'm not trying to toot my own horn here, and you don't have to listen to it if you don't want, it was already posted in the song forum, but the following link is one such song.  The melody and verse came to me one morning as I watched the sunrise.  Of course, I had to put music to it, but you should try the technique.
 
http://www.soundclick.com/player/single_player.cfm?songid=13384346&q=hi
 
Jesse Q. Screed
 
Also, I think it is important to write songs for yourself, and not for some genre, or what you think would be popular, unless you want to be popular.  And, if you have average abilities to play instruments, as I do, it is even more important to just let it all hang out and not worry about whether people will like what you do, because 99%of the people won't like it, or care, unless of course you have been given the gift to write catchy melodies.
 
My Grandfather loved to whittle.  He would pick up any odd piece of scrap wood and try to fashion a figurine.  Nine times out of ten he would toss a finished piece on to the wood pile and start a new one, a new one that he was sure would be better.  I still remember that he was always trying.
 
Your skills will improve the more you try.
 
 

iPhone voice recorder because I commute to work every day. If I don't capture the idea, it's gone.
I also have a template setup for a vocal mic, piano, acoustic or electric guitar. 
I will start messing around with nothing in mind until something interests me.
I have lots of takes that were not played to a metronome.
I put the date in the song title and go back to listen at times.
At this point, I have more ideas waiting to become songs than not.
 
Once I get a new song idea started, I will start building the chords to a basic drum track. I will sing melody over it but without any meaningful lyrics. In fact, I will substitute actual words with guttural sounds - anything to just be a placeholder.
 
Then, as the song takes shape, I will start writing lyrics to the melody. Lyrics take the longest for me. I might work on them for weeks/months. Not in a hurry so it doesn't matter. 
Once that is all done, I start working on the arrangement of all the parts. That takes less time because I am not that good on guitar and I tend to except my playing too quickly. I have found great use of Melodyne to help me with the gross imperfections of some of my work. 
 
When all of that is done, I start mixing. That can take weeks and weeks. I am never happy with the first batch of them. My studio, headphones, iPhone, and car all tell me something different. It is all a compromise at this point. At this point, I don't have anyone to answer too but my fellow forum songwriters and myself. There was a time in my life where it all really mattered with publishing deals, album deals, filmscoring, etc. Those were the days when you did not have the opportunity of working on something over and over again for months at a time. Then, when you recorded, you had to commit to tape and move on again. Now, I have all this technology to help me. I don't take any of it for granted. 
 

Rimshot
iPhone voice recorder because I commute to work every day. If I don't capture the idea, it's gone.
 
I don't have anyone to answer too but my fellow forum songwriters and myself.
 
 gross imperfections of some of my work. 
 
 I don't take any of it for granted. 
 

 
Rim shot, you nailed it (no pun intended.)  Except I disagree on one thing, and that is this, you have no one but yourself to answer to.
 
Gross imperfections?  Have you seen my earlobes?
 
Jesse Q. Screed

Midiboy
 
 
What are some of your favorite song writing techniques? 

Beer