Should you switch? That depends. If you're not satisfied with the service you are receiving, would like more investment options than your current broker offers, want to cut down on fees (or pay more, for some bizarre reason), or are enticed by one of the freebies you see being advertised, then you should consider switching to a broker who better serves your needs.
And, of course, if you're using a full-service broker, then you know how we feel, don't you? It's time to start doing things for yourself.
The mechanics of moving an account are pretty simple, and your new online broker will provide forms and procedures for making that transfer. Don't forget to ask about any account transfer (or opening) fees -- from both your old broker and your new one. If you wish to transfer only part of your account -- that is, transfer some money from an existing account without closing it out completely -- contact your old broker to get a check cut for the portion of money you wish to withdraw.
And if you're switching from a full-service broker to a discount one, don't let your old broker talk you out of taking control of your own money.