Please DELL update the shipped Realtek sound driver for Dell Inspiron 7737 and others that have this problem to the needed version "Realtek High Definition Audio Version 6.0.1.7950" instead of "Realtek High Definition Audio Version 6.0.1.7544" or lower!
Finally fixed this. NONE of the solutions above worked for me. I have an Dell Inspiron 7737 that has Realtek High Definition audio. The latest drivers from DELL or latest I could download from Realtek site ("Realtek High Definition Audio Version 6.0.1.7541" / "Realtek High Definition Audio Version 6.0.1.7544") didn't make a difference. Skype microphone was not usable (I had to literally speak in the microphone - 1 cm away to be usable).
PREVIOUS ANNOYING SOLUTION (just in case the real solution doesn't work for everyone): previously I went in device manager, update driver, "let me choose" / "pick from available"... then selected "High definition audio" - so the generic driver from Microsoft. That fixed the problem but realtek specific things like jack sensing didn't work anymore so it was annoying. Also every now and then (when windows update happened I think) it reverted back to the broken Realtek driver and had to do this all over again or simply choose "rollback driver" once instead of update and then it would pin the driver to the generic "High definition audio" one.
SOLUTION: install this driver that is not available on either dell (for this laptop model)/realtek sites at this moment "Realtek High Definition Audio Version 6.0.1.7950". I got this from a collegue's suggestion to use "Snappy driver installer". You can find it on the internet. It showed me 5 alternative drivers, 3 of which were "newer, less optimal and unsigned", 1 on which was "old and unsigned" and 1 was "newer, less optimal and signed". I picked and installed the latter and it was 6.0.1.7950. Well it seems that this "less optimal" driver fixes it. Now ppl. can hear me on skype just like in the good old Windows XP SP3 days :).
I think this will help loots of ppl. - I have the exact same problem on an older Acer laptop but I will try fixing that later today. It would save days for many many ppl. around the world if Microsoft/Dell/Realtek actually would use the correct drive for these laptops! Thanks "Snappy driver installer"!