Anti-Zionism means a lot of things to different people, but the purest definition would be along the lines of this:
A rejection of the idea that a Jewish state, by and for Jews, should exist, and non-Jews living in that state have unequal rights.
By that definition, I'm somewhat anti-Zionist - and I've been to Israel, and loved it there. Great, friendly people. But they really need to stop d*cking over the Palestinians, and believe the ideal solution is a state that wholly recognizes the rights of its minority populations (Arab Christians, Arab Muslims, Druze, hell, even Ethiopian Jews).
That said, Israel really needs to solve its ultra-orthodox problem. Everything else is tied up in that.
I'm a Jew, and I support this. They should put aside hate, and solve their problems by compromising. Both Israel and Palestine have faults. But both sides should agree to a two-state solution, Israel and Palestine. The Israeli and the Palestinian people need to vote the current anti-peace extremists in power, and vote in a Sadat for the Palestinians and a Rabin or Begin for the Israelis.