The first thing that you need to do is to convince him that you're still important to him. If you're asking can I get my ex back, then you obviously don't want to lose him forever. He also needs to see that he does not want to lose you forever as well. This is the best way to see if you stand a chance or not. It may seem difficult to show him this, but it's not really that hard if you know what steps to take.
If your concern is can I get my ex back, then you should consider trying to be a good friend to your ex boyfriend first and foremost. Show him that you care about and understand his feelings. Show him that you can be in his presence without starting drama. Joke about the situation and be light hearted to show him that there are no hard feelings. Friendships are healthy and happy relationships. If you are asking can I get my ex back, then you are going to want to create a positive healthy friendship first, and see what develops or re-develops in time.
Another consideration to make when asking yourself can I get my ex back, is that communication is absolutely vital. You want to make sure that you are friendly and kind, and that you communicate well with him. Don't let him think that he can get you back all at once, though, because a little bit of playing hard to get is a good way to go. Although you are asking yourself, can I get my ex back, that does not mean you have to play as if you are desperate.
Whatever strategies you decide to pursue when addressing the question of "can I get my ex back?", it is really vital that you do not act or look desperate. You need to be able to show your ex that you are okay with everything that has transpired, and that you are capable of moving on if need be. After all, the important thing is to be friends now, and to wait and see what develops over time. Don't be afraid to have a separate romantic life from your ex, showing him that you're just fine with the breakup - As this may draw him back to you more quickly than you thought possible.
So the answer to can I get my ex back is yes, you probably can as long as you know what steps to take.