What to do as the parent is the REAL question though! The tone you set in your home with sibling spat will ultimately define you. Here are some ideas to help you out.
#1 - STAY CALM
You knew that was coming, didn't you? Yep, you have stay calm no matter what. If you yell, you are just giving in to the stress and conflict that are brewing, a recipe for disaster and frustration.
#2 - KEEP OUT OF IT
You should let your kids try to solve their own relationship issue. Step in only when there is danger or physical harm.
#3 - DON'T TAKE SIDES
If you do have to get involved, you need to stay unbiased, no need to figure out "who caused it". The main thing to keep in mind is that it takes "two to tangle" so dealing with both kids equally should be your course of action.
#4 - USE ENERGY DRAIN
Just like whining, sibling rivalry surely drains energy in a household. Ugh! Does it ever! Start by handing out a good does of EMPATHY:
"Gosh, all that arguing is really draining my energy. This is so sad."
Then deliver the ENERGY DRAIN consequence:
"I guess you two will have to figure out how to put energy back in me. How about taking a look at the list on the fridge? Let me know which one you each decide."
The trick with Energy Drains and sibling spats is to just give them, don't start taking sides or anything, just hand out the consequences and follow through. Feel free to be too drained to make dinner or drive kids to their soccer practices. ;)
If you need a list of ideas look on my website under "Parent Resources".
#5 - SEPARATION
If the kids are angry and out of control feel free to separate them until they cool off:
"Wow, this is so sad. It really looks like you two need some time to cool off. Go ahead to your rooms and come out when you're feeling better."
You'll still be using #4 above after they cool off but feel free to get them calm first.
#6 - FAMILY MEETING AND BRAINSTORMING
This is the WOW in being a family if you ask me -- solving problems and modeling how to do that with your kids. After everyone is calm and at a time in the future, Sunday nights might be a good time, hold a Family Meeting and talk about ways to communicate and avoid sibling conflicts. If your kids are always fighting about Legos, you'd maybe set up some structure for who gets to use which ones first on a rotating basis. If one kid is taking too long in the bathroom, set up parameters for that. If one kid is staring at the other just to piss the other one off, feel free to role play how they might interact differently.
One last thought about Family Meetings is that you shouldn't just have one, have another a week later to check in to see if there is more tweaking that can be done. I often coach families to use Family Meetings to solve other problems like getting out the door in the morning or setting up bedtime routines.
Here's also a nice article I found on Sibling Rivalry