Although flexible nibs can sometimes be special ordered, the nibs on nearly all modern pens are quite rigid. The line they leave is pretty much the same no matter how they are used or who uses them. With a more flexible nib, line width varies with pressure; strokes are thick and thin, expressive and personal. Writing with a good flexible nib is a joy. Writing with a rigid nib is sometimes said to be like writing with a nail.
Flexible nibs are not for everybody. Those who press hard can destroy a flexible nib, and lefties often have problems with them. Writers that consistently push flex to its limits can also leave nibs fatigued and distorted, nibs that would have lasted a lifetime with a more delicate touch. That is why penmakers now stick with rigid nibs, which are not only more resistant to abuse, but also are much easier to make.
Vintage pens often sport wonderfully responsive flexible nibs. The best are to be found in pens of the era before widespread use of carbon paper 1920s and earlier in US-made pens, much later in pens from England and elsewhere. Waterman, Wahl, and Swan are good bets for flex, also Conklin crescent-fillers and virtually all eyedroppers. Conversely, some models only rarely sport flexible nibs (American-made Duofolds, Vacumatics, post-1920 Sheaffers), and so fetch a substantial premium when they do. It should also be noted that few modern "flexible" nibs compare with the old-timers when it comes to resilience. Most new-made flex nibs are more soft than springy, which gives a distressingly mushy sensation in place of the lively action typical of a fine old nib.