Back in the day it was possible to get an entire PhD for cloning a gene. (See the person at the bottom of this list, for example.) This is because it was hard. Before PCR... well, I don't really know how genes were cloned, but I've heard stories. It involved a lot of restriction enzymes to cut DNA at specific spots. You often had to make your own. Sometimes this meant you had to discover a new one, and then make it. Apparently people used phages- viruses that prey upon bacteria- sometimes. Beyond this I would have to look it up in a book. An actual, physical book. Anyhow.
Nowadays I can clone and sequence a gene in two weeks at the most, or a week if I'm efficient. The whole genomes of many, many organisms are publicly available. Primers can be bought for about $4 each. Aging thermocyclers abound in every corner. Sequencing became immensely cheaper as well, because it's done by PCR-based methods now. The benefits of this are immediately obvious. If a researcher wants to do something to a gene, well, she can PCR it up, make some mutations with primers, and pop it back into the organism. If she wants to find a mutation in a human gene, extensive mapping to figure out about where it is will still be necessary, but then she can sequence the whole darn gene if she feels like it.* She can also knock out a gene by making a long DNA sequence which will replace the normal gene. Knockout mice are so widely used that it seems every lab has one, on the theory that if you take away the gene maybe then you'll know what it did. (However, frequently the answer is 'kept it alive.' Less informative.)
PCR made it possible to know a great deal more about your DNA sequence, in much greater detail than ever before. It made genetic testing routine and genetic work in organisms an everyday event. It made genetics and therefore science move a hundred times faster. Without PCR, I'd still be slogging away trying to stick little pieces of DNA together with the equivalent of Elmer's Glue.
On an unrelated note, when I was in college, I went and xeroxed this article by Kary Mullis (the inventor of PCR). Tragically, it is unavailable online. However, I will summarize from memory. "Duuuude. I was so high, driving around in California and acid is totally mind-blowing let me tell you, and there were hills. And I was driving through the hi9lls and my mind was like totally blown and I saw the lines on the road and they were going back and forth and back and forth in this wavy line and I was totally like that's like DNA because it has two lines, see? And then I thought, duuuude, polymerase is like my car moving along the road and then I went back to lab and sat around with a bunch of waterbaths and amplified a gene and it sucked but then I was rich and famous. The end." If you have the opportunity to read the original, I suspect your reaction will be like mine: "I can't believe they published this."
On an even less related note- do you think drugs were maybe, just maybe, involved?:
The raccoon spoke. ‘Good evening, doctor [Mullis],’ it said. I said something back, I don’t remember what, probably, ‘Hello.’ The next thing I remember, it was early in the morning. I was walking along a road uphill from my house.”Yep. I bet you were, buddy.
*Older methods involving sticking bits of DNA to chopped-up bits of genomic DNA can still be useful here.