As others said, it depends on the player's personality and possibly if he's married with kids.
I remember Todd Marchant using his NTC to block a trade to Anaheim in the Sergei Fedorov deal. It wasn't anything against Anaheim, Marchant and his wife had a three young kids and they had just gotten settled in Columbus. To get around the NTC, Marchant was waived and Anaheim claimed him. Marchant stayed with the Ducks organization for the next 15 years.
Edmonton thought they signed Michael Nylander in 2007. But allegedly Nylander's wife wasn't too enthused by that and he went to Washington instead.
Thomas Vanek left money on the table by turning down the Islanders in order to sign with Minnesota (his wife was from there). Aside from the money, part of the allure of Zach Parise returning to Minnesota was that his kids would be geographically close to the grandparents.
Scott Stevens signed with St. Louis in 1990 as he and his wife were ready to start a family. Then a year later, he was awarded by an arbitrator to New Jersey as a result of St. Louis signing Brendan Shanahan. Stevens was pissed since they spent time/energy on their dream house in St. Louis. In 1994, Stevens signed an offer sheet with St. Louis with the desire to move back. New Jersey matched and Stevens has stayed since.
On the flip side, I did enjoy some of the stories that Scott Gomez told of his early years on the Devils. Seemed like the bachelors had a lot of fun on road trips.