As cliche as it sounds, my memories are what makes me who I am.
If you know it sounds cliche, why don't you think of more original phrasing. And yes, it is cliche.
Looking back at my past is something that always will affect me just as much as my present.
As is this. Or perhaps trite would be a better word?
Nothing is able to create an emotional high for me as much as spending time with friends and playing a good game of paintball does.
Spending time with your friends makes you happy! Shocking!
And nothing is able to drive me to an all-time low like thinking about how regretful I am that I never really spent time with my Grandfather before he died.
The old loss of a grandparent made you sad! Your emotions are so wildly different from anyone else's! Thank whatever deity you believe in that you explained them to me. Also, the loss of grandparent is only slightly less common, and hence dull to read about, as a topic for these sorts of essays than the loss of a beloved pet.
All of these sometimes bitter, and oftentimes sweet memories have affected both my goals and my aspirations. Without the experiences that I have had, both good and bad, I would be a completely different person.
And back to trite, general statements that tell us nothing about you.
So far into my seventeen year old life, nothing has affected me so much as the death my first dog Mika,
Oh, dear God, that's it! I stopped at this point. You actually are going to write about the death of a beloved pet! I was worried about my previous comment on the grounds it might seem like trivializing the death of your grandfather, but you actually did find the loss of a pet more worth writing about.
You need to capture the reader's interest right way in this sort of essay, and your current introduction doesn't do that, to say the least. If you must write on this topic, launch into it directly. Also, make sure the essay says something good about you, rather than about your dog, as it is you, and not the dog, that wishes to be admitted.