At what age should I encourage my kids to go out and find a job (be it part-time or full-time) and start to earn some money and have a taste of what working life is like?
If you want, this can start very early. You can "employ" them yourself for chores that are outside of the scope that you expect. These first jobs will help them understand that they can earn extra if they are prepared to work for it.
When they're old enough that you can teach them how to --
then teach them proper operation and tell them what goal you expect. Pay them according to how well they achieved the goal.
Torben's answer is a fantastic answer. I'm not sure how realistic it is to think that a child who is younger than a teenager is going to be able to get a "real" job what with child labor laws and whatnot. I've had students as young as 15 with part-time after-school jobs, but they had to have their parent's written permission. You might want to check with your country's/state's laws regarding employment of minors before you start pushing your child too hard.
From what I have seen with my students, many teenagers (15 years and up) really want to go out and find a job so they can make their own money and not have to depend on their parents for everything. It's almost a rite of passage here. You can certainly encourage your child to find other small jobs that will earn him/her money before he/she is legally able to go find a job working for a company. Besides earning money around the house, perhaps offering his/her services in the fall to rake the leaves of people in the neighborhood, shovel the walkways/driveways, babysit, etc. Obviously ensure that he/she can accomplish these tasks well first before offering the services to other people. You want to reinforce not only doing a job, but doing it well, and if he/she doesn't do a good job he/she won't be asked to repeat the task.