I know two people who have had several abortions and neither one seems to have any problem getting pregnant. If you didn't have any complications and made sure to follow up with your dr after then it shouldn't effect having a healthy full term pregnancy.
If your really worried about you should talk to your dr at your next annual pap smear.
If you don't want to get pregnant again right now you could always try one of the long term birth control options such as the IUD. That can last for a few years at a time.
I had a friend who had 2 abortions and hasn't gotten pregnant since. She went for testing at her docs and they said she's now infertile due to the build up of scar tissue.
So yes it can affect your chances of conceiving.
Lately I've been reading that it is a myth that there will be problems with future fertility after abortions. I'm not sure what the truth really is but if it is done in an unsterile environment or if it isn't done properly then you would think that there could be future problems.
I agree with the above that you should seek out a doctor and get on birth control or at least try to prevent even with a condom if you aren't thinking of TRYING to conceive any time soon.
Abortion is not a form of birth control. Please go to your doctor and get on some form of birth control, such as the pill, IUD, shot, or so on. Because you have already had 3 abortions, it is very possible that you have scar tissue built up inside of your uterus, which can make it very difficult to conceive or carry a baby to term. Look into birth control now to prevent a future abortion from happening again.
There could be problems. One of my friends had an abortion and it took her almost 5 years afterwords to conceive naturally. My suggestion is get on the pill of something since abortion is not a form of birth control.