+1000..... I've never found a product that will remove pops/clicks from vinyl without touching the music. I've used everything from Cedar to Izotope. That being said, I've found the higher end turntables/carts and phono pre's, and a good KLAudio clean allow for a silent (or near silent) transfer. People mistake my vinyl transfers for tape transfers!!
I largely agree with this. Even though most of the programs have an "inversion" function, I'm not convinced they don't touch the music, however small the effect may be. It is very easy to create a test scenario where you run a segment through the software, invert it, do not hear any music but then when you actually do the processing, the music is very obviously effected, sometimes dramatically. It is for this reason that I largerly eschew them as Bruce appears to. For my own part, after I transcribe a given side, I will run through it visually, place a marker on any obvious glitches then fix them up manually by either re-drawing the wave form with a pencil tool or using interpolation very sparingly, depending on the situation. I will still use software for the final touch, but at an exceptionally conservative setting that is so low I have difficultly hearing any effect on the music even though it still exists.
And as Bruce says, the right turntable, cartridge and cleaning regime / equipment will make a world of difference.
I have, however, come up with some extremely challenging situations in my time. They are very difficult and time consuming to fix but there is a lot of pride in getting it right. In a relatively recent situation I was left with a situation where there were some severe places of non-fill. Anyone who knows how horrible this sounds will tell you that fixing it transparently is almost impossible. It is pretty easy with a mono recording if one channel only is effected since you can simply copy and paste the unaffected channel onto the effected one (one reason I will stick to using a stereo cartridge on modern mono reissues - once everything is perfect I will take the "better" channel and paste it over the "worst" one so that I have "perfect" mono as an end-result). Stereo is far more difficult. So in this recent situation I actually went to an alternative source (24/192 source files), spent quite some time massaging those with level changes and some EQ until it matched as closely as my ears could tell the vinyl that I was transcribing. I then created a noise floor file based on the existing noise on the vinyl and mixed it with the massaged digital file. I then painstakingly mixed the digital bit over the stuffed analogue channel and the result was so perfect you would probably have to donate your ears to science if you were able to hear what I did and where I did it.