Some of my favorite photographs are ones I snapped at unconventional times. Have a camera close at all times and don't hesitate to use it. Nearly every time that I did not have my camera with me I have missed capturing something special that I have regretted.
My strategy: Have a camera handy at all times.
My advice: Take photos even when you aren't sure that you should.
I decided to pull out my camera when my dear daddy was spending his final days on this earth. We kept a round-the-clock vigil with him for three days and nights around his hospital bed. The photos I took are absolutely precious to us, as they have helped us savor a very rich time as a family.