First rule of networking: always keep in touch! This means reaching out to your contacts on some major holidays and even their birthdays to show your sincerity in wanting to keep in contact. If you're not keeping up with your communications, you may lose your contacts. And if ever you need their help (perhaps for a job lead), it would look bad if you reach out to them only when you need to call in a favor.
It doesn't even have to require much effort. Start by opening an Excel sheet and writing down all the people you need to keep in touch with as well as all of their details. Don't worry about the tediousness of the task, you'll definitely be using the contact sheet over and over again in the future. Then, all you need to do is craft a generic Happy New Year greeting, and tweak it slightly to personalize it for each recipient. Choose whatever delivery method suits you best — ecards, traditional handwritten cards or emails. No matter how you want to convey your message, your effort will be noted. Remember, New Year greetings are small acts of courtesy that really go a long way!