You can do a lot with what’s built into a new iPhone, iPad, Kindle Fire, Android tablet or digital music player. They come with a built-in Web browser, calculator, calendar and email program, as well as ways to keep track of your contacts and send text messages. But the really great stuff is still waiting to be downloaded.

Apple’s App Store — for so-called “iOS devices” like iPads, iPhones and the iPod Touch — and the Google Play store for Android — Samsung Galaxy phones and Nexus tablets — contain literally hundreds of thousands of apps (short for “applications”) that extend the capabilities of that new plaything.

Choosing the right ones can make a gadget more useful and fun. And best of all, many apps are free or very cheap; less than $5 is typical for even the most elaborate ones.

Here are some suggestions for must-have downloads, especially if you’re new to mobile touch-screen gadgets. Not all apps are available on every platform.

UTILITIES

The Web browser on your device may be fine, but it never hurts to have a second one in case something you’re trying to view on the Internet doesn’t display properly. “Google Chrome” is available on most platforms. If you’re on a restrictive data plan, “Opera” compresses webpages so they’ll load more quickly and efficiently. Both are free.

Check to see if your financial institution has an app. You can use them to check account balances, deposit checks using your device’s camera and transfer funds. Speaking of your money, “Mint” (free) is great for tracking your finances and spending trends.

Managing files can be a hassle on mobile devices. “Dropbox” (free) lets you securely store digital documents, including photos, online. They’re accessible to you from any computer or device.

PRODUCTIVITY

To-do list apps are helpful. I’ve had luck with a free app called “Wunderlist” (free), but some Apple users prefer “Things,” which is relatively pricey at $10 for each device you download it to. “Remember the Milk” is another popular — and free — to-do app.

“Evernote” is a must-own. It allows you to create notes that you can access from anywhere. Everything is searchable, even text contained within photos. It’s free. A premium version costs $5 a month if you need extra storage for your notes.

If you want a different calendar than what came on your Apple device, some people swear by “Calvetica” ($2.99 for iOS).

GAMES

“Angry Birds” (price varies, starting at 99 cents) is cute and addictive and available in several variations, including the recent “Angry Birds Star Wars.”

“Words With Friends” (free) is like online Scrabble, while “Plants vs. Zombies” (starts at 99 cents) is family-friendly and hilarious. Two of my favorite mobile games are “Jetpack Joyride,” a brainless thrill ride, and “Fairway Solitaire,” a brilliant mix of golf and cards. Many mobile games are discounted or priced free through the holidays, so grab them quickly.

SHOPPING

The Amazon.com app is a no-brainer for online shopping. You’ll also want to grab “Groupon” if you partake of their daily deals. You can use the app’s barcodes at shops instead of printing coupons. The “Yelp” app provides users’ reviews of restaurants and retailers.

And whatever stores you frequent —Target, Nordstrom or even drugstores such as Walgreens — each has its own app that includes coupons and special offers. All are free to download.

ENTERTAINMENT

If you’re already a subscriber to Netflix, Hulu Plus or HBO, download their respective apps. “HBO Go” gives subscribers to the premium TV channel streaming video access to pretty much every episode of every show it has aired.

If you have cable or satellite service, your provider probably has an app that allows you to set DVR recordings and stream some video via a smartphone or tablet.

For music lovers, “Pandora” is a great way to get exposed to music. “Audible” is for downloading audiobooks, and new customers get their first audiobook free. For movie information, and theater listings and tickets, try “Fandango” or “Flixster,” both free.

SOCIAL MEDIA

If you’re big on social media, you probably already are plugged in to these, but grab the official “Twitter” and “Facebook” apps if you use those services. Some Twitter users swear by “Tweetbot,” a paid app alternative. There’s also “Google Plus” and “Pinterest” (for visual “pinning” of stuff you love). “Instagram” also is a popular photo social network app that’s free to download.

If your socializing online is more along the lines of video chatting with friends and family, download “Skype.”

NEWS AND BOOKS

If you’re a heavy reader, make sure you’ve got a good way to download ebooks. Amazon’s iBooks (for iOS only) and Amazon’s “Kindle” app (for all platforms) are the leaders, but there’s also the “Kobo” and “Nook” apps and bookstores.

“Flipboard” provides news sources in a gorgeous, visual way. It allows you to see Google Reader feeds and stories.

Most major news organizations have apps, including NPR — which also provides access to audio feeds of shows and member-station live streams — The New York Times, CNN, the BBC. (The Statesman has a smartphone app and will launch a tablet app in January. For the phone app, log on to www.idahostatesman.com/mobile and scroll down to the Phone Apps.)

FOR KIDS

Your children will want to get their hands on your new electronics. The best apps I’ve seen for them include the excellent storybook, “The Monster at the End of This Book” and “The Fantastic Flying Books of Mr. Morris Lessmore” (iOS only, $4.99 each).

PBS Kids has a lot of apps for various platforms, including “PBS Kids Video” for iOS. See the full list of their offerings at pbskids.org/mobile/.

MISCELLANY MUST-HAVES

Other don’t-miss apps include (iOS): “Google Maps” (don’t rely on Apple’s built-in maps), “Remote” (for controlling Apple TV and Macs in the house), “GarageBand,” “YouTube” and “Paper” (iPad only).

Other good ones include (Android): “DoubleTwist” (like iTunes for Android), “Apps Organizer,” “Google Voice” and “Photoshop Express.”