There are a ton of mobile games out there today needing internet connection in order to be played. An example of that is Shadowgun: Deadzone, Clash of Clans, and Green Farm. Some games require you to be online in order to play while some have online capabilities but are only optional (not mandatory in order to play the game). So, the big question is, do you still bother to play online on your mobile device?
I definitely play online games on both my mobile devices (tablet and smart phone) because it keeps me calm and relaxed, especially on very busy days (weekdays). During breaktime, online games take my mind off the pains of in-between hectic job schedules and they still give my brain a bit of a workout without using it to solve problems at work. Second, it also takes my mind off the stress of waiting for the next bus and/or train arrival during rush hour whenever I have to travel to the office and back home.
I've played a handful of mobile games online, and most of them are so much more fun online rather than offline, if you're given an option between the two. I love Asphalt 8: Airborne, although a lot of phones won't play that game smoothly online because it requires a fairly strong processor. There are tons of other games that are best enjoyed while online, though.
I play Clash of Clans too although not as much as i used too. It's pretty much the only game i play on my phone although i have other games downloaded, i never really pay attention to them except for Clash of Clans. I now have a lvl9 townhall and most of my troops are maxed out on their lvls. My base is definitely far from being a noob. LOL
I have two mobile games that I like playing online. One is 8 ball pool by Miniclip which is very well made, and you will definitely appreciate the physics a lot more if you have already tried playing pool in real life. Also it's great to play some matches online because every game is different so you could potentially play it for hours and hours.