For outdoor use, put some time and energy into protecting and weather-proofing your electronics. 

Adafruit carries a few different waterproof cases. If you're just dealing with mild weather and sprinklers, you could also use a waterproof iPhone case or even a ziploc bag. If you're moving these strips around a lot or putting them someplace where they will need to resist dust and windstorms and rain, consider one of the weatherproof enclosures below. They'll keep most everything out.

The power supply carried at Adafruit is not rated for outdoor use, but for normal weather conditions I've found that it holds up pretty well. I use gaffer's tape or duct tape to tape the area around where the power cord plugs into the supply. This ensures it never gets pulled out, and also adds a good bit of weatherproofing. 

There are weatherproof outdoor power supplies available - check landscaping supply places to find these. They tend to be expensive specialty items and don't always deliver reliable power. Putting your power supply inside a plastic bag or enclosure will work just as well for heavy rain conditions.

For the strips, I always make sure to seal both ends securely with clear heat shrink and hot glue. The JST connectors are surprisingly weatherproof on their own, but for a permanent install it wouldn't hurt to also cover them with gaffer's tape or duct tape.