On the conservative and Republican side of things, conservatives are generally against abortion. More and more Republicans, especially the younger ones are coming out for abortion. Even before I crossed over, as a young Democrat, I knew of pro-choice Republicans, but officially the Republican Party Platform to date is against abortion.
On the other hand, the Democratic Party Platform stands officially for abortion. I went through a time feeling that abortion was okay, but my spiritual growth put an end to that while still a Democrat. I come across many conservatives that assume all Democrats are for abortion. That is not true, but the Democrat Party hierarchy likes to keep a lid on the anti-abortion folks within the party.
The late Robert P. Casey who was a former Democratic governor of my state of Pennsylvania was staunch pro-life. He was denied a speaking slot at the 1992 National Democratic Convention to speak on behalf of pro-life Democrats. Former President, Jimmy Carter is also pro-life and feels the Democratic Party should back away from their official pro-abortion (for any reason) stance. He said so on the Laura Ingraham radio talk program not that long ago. Go here for more.