The phrase "I have an open door policy" was very intriguing to me in my early career. As a younger staff person, I envisioned the day when I could be a supportive, empathetic manager who was able to respond to any of my employees' needs, questions, and comments whenever they needed me. I envisioned people coming to my door (which was open, of course), asking, "Got a minute?" then me leaving my work, talking with the employee, them thanking me for being such an inspirational manager, then me going back to my work and picking up just like I never left it. Ah, the naiveté.
When I actually became a manager, I shortly thereafter gave my empathetic, "I have an open door policy" speech and was ready to solve problems for anyone who crossed my threshold. Within a few months of my open door policy, I saw my own productivity drop and my frustration level rise because I kept getting interrupted by people taking me up on my open-door policy. My open-door policy soon turned into a series of random interruptions that caused me to not get my stuff done. I came to recognize that I needed to be accessible to people but that I could control the accessibility through scheduled time. Open-door means be accessible, not come in whenever you want.
I realize that I am in some ways debunking a philosophy that a lot of people subscribe to. I also don't want to be so regimented in my depiction that you think I never permitted drop-ins. Quite the contrary, I really liked the occasional chit-chat or quick questions at the right times. The "be accessible" policy means that you welcome and encourage people to come talk to you, but as a general rule should schedule time with you just as the requestor would with any other meeting that happens in your organization. Dropping in whenever the requestor feels like it shouldn't be encouraged, particularly when you're already busy.
Also, "be accessible" doesn't mean you'll just see anyone about anything. Depending on your level in the organization and your degree of influence, you can spend the vast majority of your time meeting with people that will either want to sell you something or will want an audience to air their personal grievances. When you get requests for your time, it's a good idea to ask what the requestor would like from you. You can then make an assessment of whether it is appropriate to meet with the requestor or to suggest another person the requestor should contact.
The "be accessible policy" works, it just takes some discipline on your part. Do the following to help the be accessible policy work for you:
Set the expectations up front - It's very soft & fuzzy to say "my door is always open," but unless you truly mean it don't say it. A better expectation to set is "feel free to schedule some time for us to talk." You still maintain a desire to want to talk to people, but you also set the expectation that they should find time that is workable for you both.
Make it easy to schedule time with you - I've worked with some managers who intentionally block out their entire schedule for months out and make it very difficult to schedule time to meet. The rationale I've heard is "if someone really wants to meet with me they'll get on the phone with my assistant and try to find a time that works." Yeesh, what a power trip. If you're truly so busy that every hour is blocked off for the next several weeks, then that's understandable. Just don't intentionally make it difficult for someone to see you.
Don't be afraid to ask a drop-in to come back at a scheduled time " If someone does drop in and you're unable to accommodate him or her at the time, be deliberate about asking him or her to schedule some time or to come back at another time which is better for you. You're still being accessible; you're just deferring the discussion until a more convenient time for both of you.
Keep the appointments you make - Sure, stuff happens and you need to reschedule appointments at times. Try not to blow off these informal chats too much or your "be accessible" policy turns into a big joke.
Being available to talk with people or help them through their problems is a wonderful thing. Don't feel obligated to post an open-door policy. Let people know you're accessible. Also let them know they should work to schedule time with you so you can give them your undivided attention. You'll accomplish the same goals as an open-door policy and will get your own work done to boot.