You need appropriate licensing for the service in which you operate.
On the marine bands you need a ship station license (for the boat), which conveys a call sign and a Federal MMSI. The ship station license is good for 10 years between renewals. At least one person aboard should have a restricted radio operators permit (RP) for the operator. The RP is good for life. You can use your ship station license and RP anywhere in the world (consider the mind-boggling international agreements it took to make that happen!).
On the ham bands you need a ham license. Ham licenses are both a station license and an operator license in one document. You can use your ham license ON THE HAM BANDS anywhere in US territory, international waters, or in accordance with reciprocity agreements in some other countries. See International Operating
In an emergency you can use any service. An emergency means someone is at risk of dying. It does not include running short on Grey Poupon, making marina reservations, asking for weather information (unless you are in the midst of a hurricane or cyclone), or anything else that a reasonable person would consider a convenience.
The FCC licenses are issued for specific services and any given license is only good for operation in that service: marine, air, ham, GMRS, broadcast radio, broadcast TV, cell, WiFi, etc. In the US there are blanket waivers for many services including ship's radar and WiFi and the client side of cell.
All good answers here. But a couple of clarifications...
You do NOT need either an FCC license or MMSI for operation on the marine VHF band when operating voice communications within US waters (this includes adjacent international waters. i.e. just offshore of US territories) and while communicating with US stations. (You can't talk to a Mexican station while offshore of San Diego, CA - but I doubt the FCC will send in paratroopers.) The FCC made this exception years ago to get recreational boaters off the Citizens Band - the purgatory to which they were previously consigned. There were some real tragedies when boaters couldn't reach the CG on chaotic Citizens Band.
A restricted operator license is the minimum requirement elsewhere on VHF -- but that is a minimum
level of license. I hold both a commercial radiotelephone operator's license and a GMDSS operator license, which supersedes (is "above") the restricted license, so saying a restricted permit is "required" doesn't apply to everyone. The FCC won't issue a restricted license to someone who holds the licenses that I (and may other people) hold. We had to take lengthy exams to get our licenses - and the FCC would only respond with a quizzical gaze if I applied for an RP license. I've had some heated conversations with authorities who demanded my RP license. It's kinda like demanding an Airline Transport Pilot produce his Student Pilot License.
If you are in distress, use your vessel name and marine call sign (assuming you have one) on the Ham bands. Not because you have to - if you're in distress you can use your first name if you want - but you'll be taken more seriously by the rescue agencies if they can look up your vessel information. It isn't part of the common body of knowledge for Hams to know that in a distress situation you can use "any frequency, any mode, and any power" to attract attention (I'd even try using the international aviation distress frequency: 121.5 MHz, AM modulation), so someone might yell at you. Ignore them, or better yet, invite them to come out and arrest you.
And if you have an HF SSB radio on board, remember this frequency: 14.300 MHz, upper sideband. It's monitored by Hams specifically for marine distress calls. If there's a conversation in progress on that frequency, wait for a pause and say: "BREAK - MAYDAY." They'll stop talking.
More here: http://14300.net/netinfoa.htm
. And here's an example rescue: http://14300.net/windchild.html
. The Hams there know the ropes of marine distress communications, and they'll move heaven and earth to assist you.
And in answer to the Rob Patterson's question: I suggest any of Gordon West's books. Although they are aimed at Ham radio operations, they contain plenty of general radio operating information. To practice radio operations, I suggest getting a Technician Class Ham license and practicing in your area. Also, spend some time monitoring marine channel 16. You'll hear some good, and occasionally very bad, communications techniques there. Also, if there's a Vessel Traffic Service frequency in your area, monitor that to hear how some of the pros use their radios, and you'll hear nearby bridge-to-bridge communications on channel 13.
N8QH, Commercial Radio Operator, GMDSS Operator and Maintainer