In the cowgirl's day job, she tries out different technologies, and so gets to try several tidal apps on a variety of mobile devices. The following is not an endorsement of any one tool or phone system. It's just a catalog of what I've tried, and what I like about them.
Some of these are US or region-specific. Be sure to read the details before downloading or purchasing.
iOS (iPhone, iPad)
Tides is simple. It has two panes, one for tide, one for current, which is more important for most sea kayakers. What I like about Tides is that it has data for a lot of NYC data points, from Edgewater to the GWB, to Hell Gate, to Roosevelt Island, allowing very granular trip planning. What I don't like is that it only gives you three days of data: today, tomorrow, and the day after.
Also known as Tides Near Me, this has a wide variety of data points - if you really want to know the difference between Spuyten Duyvil and Broadway Bridge, this is your app. What I like about it is that it shows the expected tidal rate, and also the start of a cycle as well as the peak of a cycle, for example flood start and max flood, along with sun and moon rise and set.
TidesApp is US-only, and shows forecast sun and moon data along with high and low tides. Tapping a button brings up a visual graph of the tides. You can look up other days, and choose from other stations "near me". TidesApp is unusual in that it has a lot of NYC-specific data sources, including, bizarrely, Grant's Tomb - I'm not sure where some of this data comes from but the Battery and George Washington Bridge data has been reliable.
This is a pretty straightforward app that pulls data from various NOAA Buoys. It will find nearby buoys and tide stations, or you can select from a list; you can store favorites for frequent use. Hands down the easiest way to check water temperature short of actually calling a buoy or sticking your hand in the water. This app also illustrates moon phases and tells you the change in mean water depth for a given tidal cycle.
Tides Planner is probably the most sophisticated of these apps, and I only run it on an iPad. It shows a graph of the tidal cycle, and you can drag along to any point in the wave to see what time that will be. I also shows low and high water depth, and will tell you when the next nearest neap and spring tides are. The reason I use it the least of all these free-ish apps is that to see anything other than "today" requires buying another license via in-app purchase. These aren't expensive, but they do add up, and I don't expect I'd get much more data than I already have available elsewhere.
Tides Near Me - Free is a simple app, showing the start of flood cycle, sun and moon rise and set. It uses an old digital clock font. No graphics otherwise though.
Currents (map overlap)
Honestly, I haven't figured this one out. It's supposed to be an overlay for Google Maps. Whenever I open it though, I just see Google Maps - no arrows or other indications of currents.
Windows Phone 8
Tide is a good app, but it's really meant more for surf, both in the locations it references and the data it provides. For example, the nearest data point I could find for New York City was Rockaway. Tide predicts wave and swell height as well as wave timing for up to a week. Oddly, wave height is given in feet but air temperature is give in Celsius.
Tides is a freemium app -you can look up tidal data for a number of sites worldwide for free, but to see anything other than today, or to save favorites, you have to buy the app. Somewhat unique is that it illustrates the moon phase in the wave graph.
This is a pretty simple graph of whatever site you pick. Favorites can be saved. Data is displayed as a graph, with the specific times of high and low, as well as the change in water depth, spelled out. One kinda neat feature is a month view that shows the tidal wave extended over a monthlong calendar. although its hard to make out at that scale anything other than "high tide looks like the afternoon that day."
In addition to the apps above, I rely on Wunderground for weather data - in part because they include wind predictions, which are also critical to a sea kayaker. I haven't found it yet for Windows Phone 8 but it is on iOS and Android: