I like to leave a few claws sharp.
All mine are outdoor/indoor cats so they need to be able to climb and grip when escaping from enemies - I feel if I clip all their claws at the same time they can lose their ability to escape, so I trim alternate claws one week and the rest the week after when the clipped ones have sharpened up again.
Yes, always keep an eye on dew claws as these often grow into the pad if unchecked, as they don't naturally abrade on the ground.
Mostly outdoor cats will wear down their front claws and bite their back claws down themselves, so don't need clipping, but older cats or those with tooth problems cant do this and may need help. All indoor cats will need help with trimming and I too have had cats who got snagged on nylon carpets, net curtains, my tights! Never had one get stuck to a wall yet though