mathematical analysis books with many examples I am looking for analysis books that can explain thing clearly and contain many good examples to help me understand the math. 
I don't possess a very in-depth knowledge of mathematics. Also, it's alright if the book is quite lengthy or pricey.

This is too long for a comment. My favourite introductory analysis book is Understanding Analysis by Stephen Abbot. It is a great exposition, and highly accessible (I think) to any undergraduate, who has seen a semester of calculus.
One particular feature of this book that I really like (which I also see especially useful for beginners, including me) is how the exercises are intertwined with the main text (most of which have hints and partial solutions). In this way, exercises do not seem insurmountable, but rather as natural continuation of thought from the ideas that immediately precedes the exercise. It is different from the traditional approach, where exercises are all appended to the end of the section, where the student will be expected to conquer them :) 
And yes, as far as I remember, this book does have good amount of examples, with the main goal of understanding (real) analysis (hence the name of the book). After/before giving rigorous proof, you will actually see most proofs "dissected" for you, in mathematical sense.
