Yes, now you can!
SimCity Finally Gets Offline, Single-Player Mode
It took Electronic Arts and Maxis over a year to make it so, but
starting now, you finally no longer need an Internet connection to
SimCity Offline Play Now Available for PC and Mac, New Details Inside
Single-Player Mode for SimCity that enables Offline Play. Starting
today Offline Play is available for all PC and Mac SimCity players
Players who choose to play Single-Player Mode will not have access to
Online-only features such as Multiplayer, SimCity World, Leaderboards,
Achievements, dynamic pricing of resources in the Global Market and
Cloud Saves. I also want to point out that saved Regions cannot be
transferred between Modes. This means that if you play a Region in
Single-Player Mode, you will not be able to play it in Multiplayer. We
want to keep the competitive aspects of the Online game intact.
Play SimCity Offline! Gameplay Tutorial
PS: As Coronus said in his answer. About you playing an online game and going offline (usually by internet issues)
Unfortunately, you won't be able to play for long periods of time in
this way. This Digital Trends
"Maxis responded that players who lose their connection mid-game will be allowed “to play for as long as we can preserve your game state” a period that will “likely be minutes."