No relationship is perfect and each has its own bouts of conflict. How you and your partner resolve the conflict defines what type of relationship you may have. One conflict that may arise is the involvement of ex-girlfriends in your boyfriend's life. Sometimes these ex-girlfriends have to be in your boyfriend's life for reasons beyond your control, and other times your boyfriend may choose to have them in his life.
Learn to trust him. While this is easier said than done, one of the most basic elements of a healthy relationship is the ability to trust one another. If you don't trust him in the first place, the relationship may not work out.
Ask him about his ex-girlfriends so you know a bit about them. If he wants them in his life, you have to know about each ex-girlfriend. Ask him questions about how they broke up and how long they were together. If the ex-girlfriend has to be in his life because of reasons out of your control, come to terms with the fact that she's there. If you can't, you should not be with your boyfriend.
Arrange for a hang-out that involves the ex-girlfriend, your boyfriend, you and other mutual friends. Plan for something casual and something public. This way you can get to know her and maybe see if she has any intentions other than friendship. It also takes the pressure off everyone if you hold something casual.
Ask your boyfriend face-to-face what his intentions are with his ex-girlfriend. Again, this is where trust comes into play with what he answers. If you can't trust him, don't be with him.