Lubavitchers actually serve in the Israeli army and Lubavitchers have referred to the founding of the Israeli state as "the beginning of the flowering of our redemption."
The Satmars (the largest Ashkenazic Orthodox group) are more ambivalent. They do not oppose the existence of the state of Israel, but they believe that it has no right to compel Jews to do anything and that it has no right to permit the violation of Torah laws. Only the government of the Messiah can truly legislate for Jews. Satmars do not do mandatory military service, etc.
The Sephardic Orthodox groups are enthusiastic supporters of Israel, and the smaller Ashkenazic groups more or less waver between more Satmar and more Lubavitch approaches to the question.
The Neturei Karta are the only ones who openly oppose Israel and support the PLO and there are maybe 1,000 of these.
They used to claim that the Satmars agreed with them, but the Satmar rebbe publicly repudiated them and their position two years ago.
>>Lubavitchers have referred to the founding of the Israeli state as "the beginning of the flowering of our redemption."
Not true. The Lubavitcher Rebbe was vehemently opposed to using that expression to refer to the secular state of Israel. The Rebbe's position is based primarily on concerns for the safety of the Jewish people living in Israel and around the world. Lubavitch supports Israel in terms of it being the home for millions of Jews but does not ascribe any holiness to the state itself and in fact views it as having delayed the true redemption.