One thing I initially liked about 5e was the skill list--it seemed like a reasonable compromise between all PCs of a class seeming to have identical skillsets (old school) and "Use Rope"-level useless granularity. A few of them felt superfluous (Investigation f'rinstance) but it was basically ok.
The Background system in 5e, whereby a player has a race, class and then a secret third thing they used to do was interesting especially if you have an established world like I do because everybody's bringing a little more meat to the table. I also works well if you often have newbie PCs played by newbie players mingling with 10th-level, 10-year veterans rich in lore.
Being fairly old-school by inclination, however, I did not like how long character generation took--especially for new players, for whom I do not like to create the impression that the game is more complex than it really is. Backgrounds seem the worst culprit here: everybody creates race, class and stats, I can do the modifier math for them, and picking spells and weapons is fun. It starts to feel stupid when rattling off the background list though--so here's what I do:
When running The Zak Hack I just ask "What did your PC do before becoming a (wizard/fighter/thief etc)?" they usually have an answer right away. Then I give them 2 skills they don't already have implied by the job and some useful job-related trinket and move on. (Demon City handles this via the "Occupational Skill" which in turn is influenced by Call of Cthulhu NPCs who all have their own job as a %ile skill, like "Gravedigger 78%").
For example last session my pal Devin made a half-elf wizard and he said he used to be a plumber so I gave him a choice of (pick 2) Persuasion, Perception and Sleight of Hand, plus a guild letter of introduction and some tools.
Then the only question was what are elves doing with plumbing but let's be real, for elf cities the fountain budget alone is staggering.