Gaming has had both a positive and negative influence in my life. Per thread I'll focus on the positive.
1. During my teens it helped me stay away from bad habits such as drugs, alcohol and cigarettes. Now I ended up doing them later in life, but I believe I would have started sooner had it not been for the gaming hobby that kept me busy.
2. It helped me get a better grammatical understanding of English with a few bad habits because of shitty translations(Yes Squaresoft I'm talking about you) and later helped me increase my fluency by fighting people over the net via Xbox live etc.
3. Gaming in general has allowed me to make a couple of really good friends who share the same hobby. Life long friends.
Pretty sure there is more, but those are the first that come to mind.