Having done scene photography for over 30 years, for training journals, department investigations, and other purposes, I find the answers that have already been provided here to be short sighted and prejudicial.
My first question is why do you do it? Are you hoping to go into public safety and are trying to get a better insight? Are you just drawn to the excitement? Do you have a "thing" for EMS professionals or firefighters? The answer is important to provide a proper answer to you.
Second, please define "interfere." Do you stay back a safe distance, going out of your way to not obstruct in any way, or do you get close enough that you're able to see everything going on, but not so close that the crews are tripping over you or have to change their path to get away from you?
Have you looked into resources in your area? There may be a fire buff group or volunteer canteen that has like minded individuals that can show you the proper way to get involved. If there isn't anything organized, I'm sure there are fire buffs that would be willing to show you the right way to go about this.
I have been a volunteer firefighter (1984-1995,) police dispatcher and special officer (1987-1990) and an EMT (1993-present,) with the last 19 of those at Boston EMS. I have encountered many buffs at scenes over the years while working, and they have generally not been a problem, since they understand scene operations better than the general public. There have been some overzealous types, but I have found that gentle suggestion of where to go so as not to be intrusive works a lot better than screaming or asking the police to deal with them. Do not get discouraged by the answers given above, there are as many people working in public safety that understand the buff mentality and do not discourage it as there are that don't.
The rules to always remember:
You are not an emergency vehicle, you cannot go through red lights, stop signs, pass by crossing over the center line, etc.
Park far enough away that if additional resources are required at the scene, you will not negatively affect their access.
Respect everyone on scene-EVERYONE. Do as your told, stay behind the yellow tape or designated line.
Be seen and not heard. Although you may be intrigued, excited, confused or some other emotion by what you see, do not allow yourself to blurt out what you may be thinking. Someone will invariably take it the wrong way. If you have questions, save them for after the incident, and ask some one-someone in the department that you may have established a relationship, or online-facebook has many public safety groups that can help you understand what you saw.
If you take photos, consider what you're doing. Gore shots serve no purpose. You may be photographing a fire scene where the owner has lost everything and directs anger towards you. Knowing how to diffuse these situations is an art that can only be honed over time, and the bigger part is knowing when to just put your camera away and leave.
NEVER argue with the police when they tell you something and just do it. Over time, you will be known as the person who doesn't cause a problem and may find that you get better access in the future as they get to know you. Yes, you may raise some eyebrows initially, but if you're doing nothing wrong, there's no reason to worry.
This article might help you a bit:
Firefighter Spirit: The Buffs Across the Street
If you're doing it for an adrenaline rush or because you're a badge bunny, my advice is to just stop now.