Jewish identity is a can of worms.
I'd like to start with the following quote from Rabbi Aron Moss at The Human Touch:
"The biggest threat to Jewish survival is confused Jewish identity. Sadly, today in many Jewish schools and families, Jewish identity is built through teaching Holocaust awareness and a fear of marrying out. The Jewish community’s preoccupation with assimilation and anti-Semitism is not the solution, it is the problem."
I find that blog posts about Jewish identity fall into three categories:
1) abstract discussion about "what IS Jewish identity"
2) what are the "problems"
3) personal accounts/feelings/struggles
As for my personal account: I just told Harley, my identity is pretty darn confused. I can recite the b-attitudes off by heart, as well as all of the books in the New Testament, but until I was 16 or so, I didn't know enough Hebrew to follow along with the amidah*. As I have gotten older, my perspective has changed, I now firmly believe that people should be able to observe/not observe whatever the heck that they want and call it Judaism. After all Shabbetai Tzvi converted to Islam, and claimed that it was the culmination of his Jewish beliefs.
Although Israel is an integral part of my Jewish identity, it isn't for 1/3 of young American Jews. QRSwave of The Truth Will Set You Free lists a few non-Zionist Jewish identities that already exist, so that you can pick your own.
And because you missed my microsoft paint magic, I have included an image of some ways that people define Jewish identity. See if you can guess what the heck I meant by each (and no, the last part isn't blank by accident, it is so that you can fill in your own).
*The word Amidah comes from the Hebrew word for standing, and refers to the silent devotion, which is part of every prayer service. During the weekday it is comprised of 18 blessings, so it is often called the "Shemoneh Esrei" or 18.