Letter of recommendation is quite culture specific but in general it shouldn't be required.
Employers who are hiring tend to value a private talk with your previous manager even more. Having a list of people who recommend you, their position and their contact information will probably benefit you, and your future employer, even more.
That being said, when leaving a company you should ask your current manager if you can list him as a recommend-er and ask him whether it's okay or not for future employers to contact him. Usually that's not a problem, especially if they value your previous work. You can still list them as recommenders, even if they do not wish to be contacted, just make sure to mention that.
If a previous manager does not wish to be contacted (some managers simply manage too many people) then a letter of recommendation would be a sweet backup alternative, but a personal talk between your previous manager and future employer is probably more valuable since it gives your future employer the ability to ask for very specific questions about you and it gives him the implication that you have nothing to hide.
Feel free to take advantage of today's social media though, like Linkedin, to request for written recommendation, but having it as the only source of recommendation should be avoided; you never know when media change or dissapear.