I mean, a snake hatches from a not very big egg, and can end up dozens of feet long.
Do they grow more vertebrae throughout life or are they born with as many bones as they’ll ever have, and the vertebrae just get longer/bigger?
I think all vertebrates start out with the same basic skeleton they keep through life and the bones just get bigger. Some of the bones also change (skulls gradually fuse together and, if they occur, kneecaps just sort of appear out of nowhere), but that’s not what you were getting at.
Same way a 6 lb baby ends up a 6’, 180 lbs man. Or a 6’ baby giraffe ends up being… triple that?
Things just get bigger. Vertebrae number are fixed at birth. Very few things are add-ons later in life.
Doesn’t crab or reptile molting count?
Those are external, not internal.
Okay, thanks for the answer.
It does seem amazing, but then I also found it amazing that giraffes have six cervical vertebra, just the same as we do – or a mouse, for that matter.
Size really does matter. 
It’s the motion in the genetic ocean that really decides who is the largest~
Count as an add-on? These are shedding of the exterior covering in one big dump, which many of us do continuously instead. What would be added on? It’s not like a six legged crab molts to become an eight legged one. Although some snakes do double their leg count each time they do it…
From zero doubled to… zero! 
Snakes and such if they are keen enough to eat well out-grow their skin and shed. Mammals shed all the time.
“Some” snakes, from zero to zero, yeah. 
What most people don’t realize is that two major families (boas and pythons) actually do have hind limbs – they’re very small, femur covered by skin, scales, and muscle only, and nestled into niches in the snake’s body. They’re protruded and used to help hold the two snakes together during mating. Two other families, together comprising the blind snakes, retain the pelvic girdle and may or may not have any external evidence of this. (And then of course we have Doper Earl Tucker. :))
All mammals have 7 cervical vertebrae…and both men and women have 12 pairs of ribs. Some of my Xtian students insisted that men had one less than women, 'cause, ya know, Adam and Eve…
Why do snakes and tarantulas (other spiders?) molt instead of losing scales along the way? I assume one advantage of my constant skin cell loss is that I didn’t have to molt.
All arthropods, including spiders, insects, and crustaceans, molt their exoskeleton all at once. This is because it really is a skeleton, and all the pieces have to fit together and work in coordination. Shedding it in pieces would mean that adjacent pieces might not be the same size and wouldn’t work together.
Snakes, on the other hand, may do it this way just because it’s relatively easy for them, since they don’t have legs. Also, since they use their belly scales in locomotion, having loose ones might cause some problems. Other reptiles, like lizards, also molt, but shed the skin in pieces.