In this day and age, scanning film directly rather than scanning prints makes a lot of sense. Making prints is very expensive and requires a lot of space and equipment. While I imagine every photographer wants to be able to make their own prints from film, for many of us it simply isn't practical. Luckily, however, there is another option - scanning! Scanning the film directly can be very advantageous for a few reasons. For one, it doesn't require a darkroom or any enlargement equipment. Two, it provides instant digitization of the image, meaning it can quickly be edited and distributed digitally. Three, it bridges the analog-digital gap very nicely.
Good scanners aren't always cheap, though, so don't expect to get off easy. I have experience with three scanners in particular, a Nikon Coolscan V ED, an Epson v500, and a Primefilm 7250u. The Epson is a standard flatbed with film capabilities, but the Nikon and primefilm are dedicated film scanners. The Nikon is by far one of the most amazing pieces of hardware I have ever used, which would explain its multi-thousand dollar price tag. I do not own one of these units, but my university has one that I can (and often do) use for free.
I do own the Epson and Primefilm, however, and they both have their advantages and disadvantages. They both cost about $250 but operate very differently. The Epson, being a flatbed scanner, can scan film as well as any types of standard sized documents/images, but due to the large size of its sensor, the quality can sometimes be lacking. The film tray it comes with can hold as many as 12 35mm frames, though, so batch scanning is incredibly easy. The primefilm can only scan one image at a time, so scanning is considerably slower, but due to the sensor's more concentrated size, it has a much greater quality.