Is it possible to get worldwide internet access on your laptop. I presume you can since as far as I know yachts seems to manage internet access, at least when they come into port.
So if it is possible, how much would it cost and how is it done?
To be truly worldwide you'd really need a mobile satellite solution, though the most "portable" (suitcase sized) ones are highly expensive while the typical motor powered mini-dish (i.e. on camper vans) is not terribly portable but may cost a bit less. Chances are you'd probably have better luck using a dialup modem connection, since global roaming dialup Internet numbers can be found almost anywhere. Further details on both these two technologies can be found here:
As for Wi-Fi and Mobile Broadband, well the latter is still too new while Wi-Fi is only available in certain Hotspot locations around the world - there's no blanket coverage. Out of all these I guess, provided you can plan your trip around the Hotspot locations, Wi-Fi is the best value, fastest and most flexible choice.
Meanwhile dialup is an outgoing technology and you'll need to do a little digging, it's also slow and you can expect the phone call charges to be unpleasant in some countries. Satellite is the only option for a full anywhere service but as already stated, it's expensive, can perform poorly and doesn't give you much of a data allowance.