3 Gift Ideas for the Day Trader in Your Life

Books are a great day trader gift. Most day traders are inquisitive and enjoy reading about other trader's successes and failures. For a well-established trader, avoid books on strategy or basic knowledge ("Day Trading for Dummies"). These will provide little additional insight but may be useful to a novice trader.
Trading psychology books

are relevant to new and experienced traders because while many people don't realize it, successful trading is mostly psychological.  Trading in the Zone by Mark Douglas is a great book for traders with some market experience. Reminiscences of a Stock Operator is a classic book written in 1923, by Edwin Lefevre. It's a great story about one of the biggest personalities in trading history— Jesse Livermore—and contains loads of humor and trading insights, despite its age.

If the trader in your life is more into the video, the List of Trading Movies, Documentaries, and TV Shows is sure to have something they haven't seen.

Most day traders have trading websites they follow, or an online subscription service they use (or want to use) to receive specific data. For this gift, you'll have to ask the trader directly what they want, as there are thousands of services available, 

Most services offer a discount if paying for the full year. This is a win-win. The trader gets a subscription service they want and you save by paying for it all at once (instead of each month).

Some traders may want advanced charting software, others may want to use a different trading platform which charges a monthly (or one time) fee. If you're the day trader, let people know the subscription service you'd like.
Another possible subscription is to a magazine—online or paper format. If you know someone who buys a magazine frequently but doesn't have a subscription, purchase a year-long subscription. This doesn't have to be a day trading magazine. There are many magazines which are popular among traders, including (but not limited to) Stock & Commodities, Active Trader, and The Economist

Different day traders require different hardware and software. Some may have a simple one monitor setup on an old computer, while others have multiple-monitor setups on high-end computers.
If the monitors are older, consider getting the day trader an upgrade, or giving them a second monitor. A second (or third) monitor makes it much easier to navigate multiple screens and conduct research. If just upgrading the monitor(s), check for compatibility with the computer as there are various connection types.
If the computer is older/slow, consider giving a gift certificate for an electronics store so the day trader can upgrade their computer.
For the trader who seems happy with their current trading setup, consider a tablet. The tablet allows them to monitor their positions and the market while away from their desktop. Most brokers now offer advanced apps which make trading on a tablet possible. An 8-inch screen or bigger is best for viewing charts.
The step up from the tablet (although having both is nice) is a laptop. A good laptop makes trading while traveling a reality. Like a desktop computer, certain traders may require minimum specifications on their trading laptop. If you feel this may be the case, or you're not sure what to get, ask first, or provide a gift certificate along with a note that the gift card should be used toward the purchase of the laptop.