Malli Karim :
You typically see screen tearing if you have over your monitor's refresh rate, which with a 144hz monitor and the newer games you wont, and in multiplayer games ( FPS games to be exact where 120hz really shines ) 120+ is more than enough. There are some rare cases of screen tearing when you are below your refresh rate but its usually game related rather than hardware, like how some people used to get screen tearing in Crysis 1 when they were below refresh rate.
I would say save money and get the 144hz without G-Sync. Now if you are loaded with cash and want to spend get the 144hz G-Sync monitor just because, but it's not necessary as tearing is not really noticeable on 144hz.
Just to be clear, any time you do not have V-sync on (or G-sync), you are having screen tearing. It is most noticeable when your FPS are near a number that can evenly divide into your monitors refresh rate or multiple evenly. There are no exceptions. If V-sync is disabled, you get tearing.
Higher refresh rates can help make it less noticeable, as it does clear your tears off the screen faster, but if you have a FPS rate that evenly divides into your refresh rate or multiplies evenly by your refresh rate (or just flat 144), tearing is still very noticeable. Even when your FPS are lower than your refresh rate, it is there. Crysis 1 was not an exception, it is just like any other game. Perhaps the reason you recall the issue was that you didn't use V-sync do to FPS issues.
If you use V-sync, you may have stutter, or extra latency if you are reaching your refresh rate in FPS.
G-sync fixes all that, but it can be pricey, at least for the first few monitors. Is clean smooth images worth the cost to you? That is up to you.