WHEW! This is longer than I thought it would be! Here's my thoughts, for what they're worth.
ASSIGNMENT: This can be a "commission" - a song requested from someone else, or you can assign yourself a job. Aine's monthly Song Challenges in this BBS is a good example of an assignment.
A GREAT PHRASE: Listen to language and you can get great inspiration for songs. I think of Randy Travis' "On The Other Hand"... a common phrase that when viewed from a songwriting perspective became a much deeper thing.
A GREAT STORY: Take a story and rhyme it. I usually write the first couple of lines and then the meter and rhyming scheme create themselves. You can use news stories, poems, or personal stories.
A GREAT JOKE: This is fun. Take a joke, write the punchline into a verse FIRST, and then write verses in front of it to deliver the set-up. I wrote a song called "Twenty Years Experience", all to set up the line "I'm not 40, I'm 20, with 20 years experience."
PURE INSPIRATION: These are always the most fun, but also the most rare. It's that "Lightining Bolt", where the song just writes itself. John McCutcheon credits "Christmas In The Trenches" as this type of song.
A DEADLINE: Can be used in combination with any of the others. Just tell yourself, "I'm going to finish this song by ____", then do it. What you have as of the deadline is your "first draft."
DON'T BE CRITICAL (on the first time around): I disagree with some of the others here in that I don't set out to write "great" songs, I just write the things....
EDIT AND RE-WRITE: ...but I WILL come back later and clean them up, edit them and change them. THIS is the process that may take years for me. I had a song I wrote on "self-assignment" called "Groundhog's Day" that didn't have a proper ending for about 14 years.
TUNES: Tunes come harder to me than lyrics. Michael Smith says to define what a song is "like", then give it a tune "like" that. ie, is it like "Steamroller Blues", is it like "Blowin' in the Wind", or is it like "Mood Indigo"... etc, etc.
SUBSTITUTION: Paul McCartney's original words to "Yesterday" were "Scrambled Eggs"... he just put in nonsense words to flesh out the meter and melody, then came back later to put in better words. Same is true the other way - you can write your words "To The Tune Of" a familiar song, then create an original tune later.
PARODY: Some folks don't consider this real songwriting - tell it to Homer and Jethro or Al Yankovic. I like writing parodies. And I like writing them as CLOSE to the original meter and lyrical content as possible. The joke is sometimes all the funnier because of the closeness. (ie Michael Jackson's "Beat It" and Al Yankovic's "Eat It".) Parodies are also usually easier than creating "Original" songs, so it's a way to hone your songwriting "chops" until you're ready to make brand spanking new ones.