Wow, because you asked, I guess we'll ignore that the last time the question came up, there were still twin towers standing in NYC.
If you coastal or daysail, you don't necessarily need more than a cheap barometer that can be calibrated to a known source, like a nearby weather station or airport. Keep in mind that if you are inland or Great Lakes sailing, you have to calibrate your barometer to the local altitude...some sources report "sea level pressure", which is not the pressure on the Great Lakes, nor is it up the side of a hill somewhere.
For those who for reasons of personal interest, expanding their seamanship, or because they are going to be sailing long passages without being able to receive info from weather buoys or synoptic charts, a recording barometer becomes very helpful. This can be analog or electric, paper roller (old style, but gives you a graph more or less continuously), or digital display.
I have aboard a now-discounted Speedtech barometer: Speedtech WeatherMate Barometer
It gives me 24 hours of readings, which is enough to track weather at a distance as well as weather that's bearing down. Basically, sharp drops or sharp rises portend wind (not always true, but frequently the case); high pressure means light winds, fair weather, and low pressure can mean dirty weather or just rain. Knowing the speed at which the pressure is changing can, with experience, tell you how near or far a storm is, how fast it is likely moving, and whether it will push the boat nicely, or is a reason to batten down.
I also have a Suunto sports watch that has a recording barometer with a three-hour trend interval, although I can manually record readings at any point. I use this frequently during periods of changeable weather to determine if it is likely to rain by a certain point in the near future. Practice and you can get better than the weather people, but only in a local sense.
Combine these instruments with looking at clouds, currents, sea state and so on, and you are essentially a one-person weather station with maybe a 50 square mile "forecast area". This is not always necessary if you can receive local or "custom" forecasting...but forecasting is an educated guess, and you are the one actually in the weather.