Producer on The Sims 4 Grant Rodiek has confirmed to VG247 that "The Sims 4 is an offline, client-based game." That means there'll be no SimCity-style DRM.
Rodiek also said that consoles are not currently being looked at as a platform for the game - for now, it'll be on PC and Mac only.
No DRM will come as relief to many. When EA launched SimCity earlier this year with a number of DRM measures, it caused a huge number of problems that made the game unplayable for many. It turned out that many of these measures were not even necessary. It seems that EA has learned their lesson, and will be keeping The Sims 4 DRM-free.