Falling water makes for a huge variety of very popular imagery - whether small cascades a couple feet across or giant falls that are 100 times as tall.  

I live in waterfall heaven, the Columbia River Gorge, a National Scenic Area that splits Washington and Oregon states. The gorge varies from rainforest to desert steppes within an hour's drive along its stunning vistas.  Having hiked and photographed here since 1985, including serious bushwhacks to gain access to remote waterfalls in rugged canyons, I've learned a few things I'd like to share about waterfall photography, with a focus on the gorge and its unique conditions... 

Preparation

• To refine my list for a new waterfall target or to verify that is feasibly photogenic, I use a number of sources. Some waterfalls are nominally impressive, but may have fairly dangerous/difficult access, or simply have too many bushes and trees to get a clear shot. Sources includes topo maps, Google Earth, local hiking forums such as http://www.portlandhikers.org, 500px or Flickr sites search by name, Google Images search by name. Plus TPE - The Photographer's Ephemeris for timing.  This step can save hours of blood, sweat and sore knees in rugged country that might be for naught without research. The "Curious Gorge' guidebook is invaluable.  Stellarium software for planning nightscape shots.
• Pre-visualize and think about gear.  If you have enough info from the step above, you might take different gear.  For example, consider falls that have a cave behind the waterfall...  I have used two LED panels to light the roof of a huge cave even though it was an afternoon shoot, and captured some really nice rock texture instead of a black silhouette looking out.  Lens selection is also vital. And panorama gear/technique is often useful, because the Gorge has some TALL waterfalls, with BIG ampitheaters. Often the ampitheaters will have interesting columnar basalt and brilliant yellow or orange lichen covered rock faces.
• Consider the wind, which the Gorge is famous for. Windsurfers come from all over the world. On windy days, seek out waterfalls that are deeper in the gorge's side-canyons.  Otherwise, you may get ferns that look like green blurs. Or forgo the silky water look and shoot a quite fast shutter.
• In the gorge, you can run into poison oak, especially in the drier eastern end of the gorge, so learn what the leaves look like before you go!

Equipment

• Super-wide lens is often important to add depth and perspective, especially on the very tall waterfalls i the gorge is famous for.
• Tripod - a solid one. With pano gear is often useful, for horizontal panos, and often, vertical panos.
• Neutral Density filters - essential for daylight shooting to slow down the shutter enough to get that silky water look. A range of filters or an adjustable one.  I use 4 and 8 stop ones.  For both my super-wide zoom and wide to med tele zoom.  Not needed if you want a stop-action look.
• Polarizer filter:  Often essential to knock down the hot spots/glare off frothy white waterfall sections, and the glare off of waxy leaves, such as the glorious green ferns in the western half of the Gorge, that aren't so green in your photo if they're shiny! This foliage glare is easy to miss on a DSLR LCD panel unless you zoom way in.
• Fairly often, there will be white/glaring sky at the top of the falls. Either compose tightly at the top of the falls to omit the sky, or use a graduated density filter to tone down the overbright sky. A 3-stop hard or soft can work often enough.
• Lenses:  at least a super-wide zoom lens (full frame 16-35mm or APS-C 10mm)  I often use my full-frame 24-105mm.  I less often use my 70-200 zoom but it has been essential at times.  Look up the diffraction curve for your lens. Know what you can get away with for max depth of field / small aperture.  My pro Canon wide zooms can shoot at f16,  but f18 and above causes a bit of diffraction/softness. 
• Remote shutter release or self-timer: Essential for sharp images.  
• For trained climbers: Depending on the terrain, I may carry a climbing rope and even harness and rappel devices/ascenders.  I'll quite often carry a short rope for safety on the edge of a ravine/cliff to get to the best camera location, even if the approach is a nice safe trail.  There's lots of safe vantage points by many Gorge waterfalls, but lots of others are guarded by wild and steep terrain. If you aren't trained for dealing with those steep situations, stay away!
• Hiking gear/Lights:  Always take the hiking 'ten essentials', especially a headlamp, unless you're shooting the many roadside or paved trail access waterfalls in the Gorge.   Use good hiking gear, footwear and clothing (eg not cotton) if getting away from the road/paved trails. Gloves are useful for tree-rappelling and catching yourself on scree slopes.  A pack that stows your tripod leaves both hands free for rugged terrain.  Rubber boots can be useful for fording streams or shooting from in the stream.
• Maps. Always take a printed topo map if going away from the road or the paved trails.  A GPS is a good idea too. Every year, people get lost overnight or fall down cliffs when they get lost and try to take shortcuts.  There are networks of gorge trails that can be confusing in dense forest.
• If you have to get into the misty blow-back area close to a falls for a shot, a camera-jacket and a microfiber cloth to throw over the lens can be very useful. Check for water drops often. Wait for a break in the mist, take off the cloth, shoot, put back the cloth, wait for another lull in the gusty mist. Spring runoff can result in powerful misty gusts.
• There's a lot of brush in the gorge. Sometimes branches that are in the way can be tucked behind another branch or your leg and released after the shot.  Sometimes downed/dead branches can be easily moved.

Capture Techniques

• Sharp things: Use a quality, solid tripod/head combo. Hang your pack or mesh bag of rocks from the tripod center post. Use low ISO. Use ND filter and/or polarizer depending on light levels, glare. Experiment with shutter speeds to get the silky look to the water without losing too much of the character and detail you want. Or go for stop action with fast shutter/higher ISO. Use your remote release or self-timer.  Use Live Image mode or mirror lock-up. Beware of vignetting from stacking too many filters on super wide lenses... take off your UV filter if need be.
• Look for promising applications of pano technique.  I've used horizontal-only panos, vertical-only panos for tall falls, and double-row panos depending on how big and photogenic the fall's ampitheater is.  I've used a ball head for this, sans pano attachments, but it's easier with pano head gear.  You can also use panos for focus layering. Grab that outflow stream and mossy boulders detail way up close, then tilt up to get the waterfall and refocus for distance. Often PS Merge does a nice job without having to use manual layering or focus layering software.
• Mostly I use aperture-priority and shoot at f16 or so depending on your lens diffraction curve, for maximizing depth of field. Unless you want to shoot stop-action then use a fast shutter and higher ISO. Sometimes windy conditions dictate faster shutter.
• Bracket a lot.  Bracket exposure, bracket the amount of shutter water-smoothing,  bracket your focus sometimes.
• ETTR: Expose To The Right. Check your histogram and make sure you're shooting to the right edge but not beyond. This will give you the most latitude to recover the deep shadows. Having a few specs of over-white water is fine, which can be brush-corrected in post or left as-is.
• Take your time in capture. Get lots of angles. Zoom in for a different composition.  Put down your camera and look around, think about clambering up one side or another of the fall's ampitheater.  Ignore the waterfall for a few minutes and walk down the the stream, look back up for a stream focus shot. Straight-on waterfall shots are often the least interesting. Go to the sides. Get behind the falls in a cave and shoot out. Panos can be great.
• Wind and patience. The gorge is famous for it's winds - a mecca for kite-boarding and windsurfing. Sometimes you need to wait for gusts to die down to avoid blurred foliage, or a better look for tall wispy falls. Or speed up your shutter. Or choose a deep side-canyon site. Even a quarter mile hike up certain side-canyons can almost eliminate wind.
• Light Source: Overcast days are great (waaayyy too common in Oregon :-), or golden or blue hours, but sometimes sunny days can work too, especially with HDR technique, and god rays coming down through the trees, or illuminating mist, even rainbows in the falls' mist can be found.
• Tidying up: Look for things that are odd, distracting or that might be improved. Examples. Remove a piece of litter. Tuck a branch out of the way. Splash some water on stones to bring out their colors.  Place a few autumn leaves on a  foreground rock.
• Nightscapes. Use light-painting and/or moonlight to get some starry waterfall shots. (That's a whole 'nother topic in itself.)
• Kayak drops:  Oregon and Washington including the Gorge have one of the highest concentrations of 'huckable' big falls anywhere. Very photogenic. See my other blog post on action-composites for this type of shot.  Kayak forums are a good source of leads for the best drops. Access to some of them can be challenging though; research first.
• Timing:  Spring snowmelt in March and April provides thundering falls big water volume. Flows in the Western half of the gorge are year-round for most falls. Some falls on the drier eastern end get pretty meager by late summer.  In Dec/Jan, cold east winds can freeze things up very photogenically.
• Wild things:  Be on the lookout for Chanterelle mushrooms!  Even in November I've bagged several pounds nearby to a waterfall shoot, though October is best.  Cougars are present but VERY rarely seen in the gorge, as they're quite few and shy and there's been zero attacks on humans.  Bears are also very unusual. In winter, you can find lots of bald eagles at the Klickitat river. Spawning salmon can be seen Spring and Fall at several locations. Early Spring has awesome wildflowers. Poison oak however is pretty common especially in the eastern end of the gorge, and you won't grab a spiny devils club stalk twice. 

Post-Processing

• Lightroom/PhotoShop is assumed here.
• Use HDR post-processing if appropriate. but avoid settings where the falls' water gets blued-out, or too smoothed out. Or layer in the waterfall separately. PhotoMatrix tends to do this.
• When not using HDR, you'll find LR's Highlights slider (to the left) and Shadows slider (to the right) invaluable.  Also the adjustment brush is great to knock down over-bright sections of white frothy water, or bring out overly dark shadowed areas.  
• Water detail: Experiment with LR's clarity slider, the blue/aqua saturation, and blue/aqua luminance, maybe a touch of exposure sliders -- to recover color and definition into the water, that may be over-whitened from a slow shutter.
• Moss: Experiment with green saturation and luminance sliders to achieve the fabulous luminous/saturated moss green you saw with your eyes. Don't overdo it though.  Luxurious green moss is the essence of gorge falls images.  Adjust sharpening when zoomed in on the moss as moss makes a great target for these adjustments. 
• Sky: For overly bright sky at the top of the falls, try using the gradient or brush tool to darken it. Or cheat and layer mask in a nicer sky behind the trees at the top ;-)