First Class is worth its cash mostly for longer flights. For a puddle jumper flight coach is more advisable. The only people I've seen in First for short flights are those who can really afford it (or think they can) and people with back problems or those who do not 'fit' into the regular coach seats. Yes, those.
However, for transatlantic flights and the likes, First Class is the way to go for the following reasons:
Comfort. Depending on the airline, First Class seats range from comfy to dreamy. Extended legroom, increased width and deeper cushions make the sitting experience bearable. Besides that they lean back further and give you more comfort when sleeping -- some seats even turn into real beds. Also, during the flight it is easier to get up more often and stretch your legs. Some of the truly first First Class flights also offer additional space -- aboard some 747s for example -- such as a lounge and bar. Boarding time is also reduced and you get on and off quicker. Some airports even have First Class-only terminals and waiting lounges, so the comfort may begin even before boarding.
Privacy. Less people means less crowding. Especially at the toilet and when it comes to getting the attention of the flight crew. The only people you may run into on the way to the toilet are the few other passengers and the pilots. Not having to be around the noisy families in coach is also a blessing. The same goes for having individual screens and personalized entertainment, environmental controls and in some airlines each seat turns into a sort of private cubicle.
Service. The chief flight attendant or cabin manager, called the Purser, runs personally the First Class area, so you can be assured of the most personal attention. Not that they don't want to take care of the coach cattle, but serving an extra drink to someone sitting five feet away is easier than to someone halfway down the plane. Also, maybe it's just me, but I have had the impression that the crews in First are often more physically attractive and less stressed. Or maybe they are more attractive because they are less stressed. As it were, depending on the carrier, crews do prefer to work in First as opposed to coach.
Food. Airline food does not exactly enjoy the best reputation. One wouldn't know, flying First. The selection is larger and the dishes of higher quality. Most of the drinks are also probably included and you don't have to pay extra for everything -- since you are already paying extra.
In conclusion, First Class is for those seeking real comfort, not bargains. Some of the best airlines in this area are Europeans and Asians -- although nobody beats the Middle East airlines.
Emirates First Class cabin