We're having a problem at work: we're trying to schedule work so that we can assess time scales and get deadline dates.

The problem is that it's difficult to plan for a project without knowing everything that's going to happen.

For instance, right now we've planned all our projects through the start of December, however in that time we will have various in house and external meetings, teleconferences and extra work. It's all well and good to say that a project will take three weeks, but if there is a week's worth of interruption in that time then the date of completion will be pushed back a week.

The problem is 3 fold:

1. When we schedule projects the time scales are taken literally. If we estimate three weeks, the deadline is set for three week's time, the client is told, and there is no room for extension.

2. Interim work and such means that we lose productive time working on the project.

3. Sometimes clients don't have the time that we need to take to do the work, so they'll sometimes come to us and say they need a project done by the end of the month even when we think that the work will take two months - not to mention we already have work to be doing.

We have a Gantt chart which we are trying to fill in with all the projects we have and we fill in timesheets, but they're not compared to the Gantt chart at all. This makes it difficult to say "Well, we scheduled 3 weeks for this project, but we've lost a week here so the deadline has to move back a week."

It's also not professional to keep missing deadlines we've communicated to the client.

How do other people deal with this type of situation? How do you manage the planning of projects? How much "extra" time do you schedule into a project to account for non-project work that occurs during a project? How do you deal with support issues and bugs and stuff? Things you can't account for during planning?

UPDATE

Lots of good answers thank you.