I have a niece that is smart, funny, and precocious. I love to talk to her on the phone, and believe me, she could talk forever. I decided to get a book for her and my sister called Q&A a Day for Kids: A Three-Year Journal available at +Amazon.com. It really could be used with kids at a variety of ages, although perhaps about 4-10 may work best. The parent can fill in the writing, or the child could write their own answers.
One nice thing about this way of capturing your child's thoughts and comments, is that this book offers the prompts of specific questions. This may generate even more interesting answers. Of course, it does not chronicle the more spontaneous gems we all love. Each day has 3 spots on the page to answer the same question. Theoretically, the same child, will answer the same question across 3 years and see how the answers differ.
I also wonder if it would be fun to chronicle a different child in those spots. For example, my other sister has 3 children, and she might enjoy comparing the oldest boy's answers with the youngest for example. They all 3 have such unique personalities, that I think that would be interesting. Examples of questions include: "What is the best thing about your life right now?", "What is the last thing you built/made?", "The best thing about being a grown up is...."
Another thing to consider are apps for this purpose. One app someone recently recommended to me is the Posterity app for capturing family quotes. It currently costs $1.99 and has gotten good reviews so far. Parents seem to enjoy the photo option that joins with the quotes. Many say they are wanting a video option to put capture their child's thoughts as well.
Another way to chronicle your child is to take videos of him or her in action and upload the videos as private +YouTube entries; these can then be shared with a few special family members and kept in your YouTube account for long term keeping.
And finally, there is the photo book option. Many internet sites offer photo books for you to create and order (e.g., +Walmart, +Shutterfly, and Michaels are just a few options). If you include your wonderful quotes, along with pictures, this would make not only a great memory book (imagine giving a copy of the books to your kids at their graduation, wedding, etc), but also a great gift for grandparents and other family members.