Why Does my car hesitate, almost wants to turn off while driving

This is not a relationship question, but I figured since I take some time to answer some questions here, maybe some of you can return the favor if you are mechanically inclined. I like to tinker with cars, but cant diagnose the problem very well...
I have a 99 Ford Mustang cobra standard transmission. It turns on fine, but when driving, the car starts hesitating and I try downshifting so it wont turn off. I also noticed that if I shift to neutral and quickly turn it off and then back on, it will fix the problem temporarily. I thought it was the fuel pump so I replaced it along with the fuel filter, but it didnt fix the problem.
Thank you for taking the time to read this, and if you have any serious suggestions, let me know. Thank you