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Pyth - 6 eo/QNQ Try it online. Expects input on stdin like [4,3,1,0,6,1,6,4,4,0,3,1,7,7,3,4,1,1,2,8]. Ties are resolved by last occurrence because Python performs stable sorts. Sorts the list by coun …

Python 2 - 18 max(d,key=d.count) Since your python answer doesn't seem to print, I expect this is what you want. Add 6 bytes for print normally.

Pyth, 31 30 FbQVbjd++*]0Z*b]b*]0--sQbZ)~Zb A pretty naive program, takes the input on stdin. This can probably be golfed more ;) Thanks @Jakube for pointing out a wasted char Try it here

Retina, 31 24 22 (?<=¶.+ )\S+(?= .*¶) 0 Saved 2 bytes thanks to randomra Try it online! There is probably a better way to do it, as this is just a pretty basic multi-line replacement. Essentially …

Pyth, 17 us-GeaYsI#GQ)S#Y The leading space is important. This filters the list on whether the values are invariant on the s function, then removes these values from the list and flatten it one le …

Retina, 34 -1* ^(1*)((?>.*?\1.*? \D))*.* $#2 Try it online! or try it with decimal input. Takes input in unary, negative unary numbers are treated as -111... and zero is the empty string. Counts …

Retina, 25 24 O^$#`[^0](?=(.*?0)*) $#1 Try it online Saved 1 byte thanks to Martin! Sort the nonzero digits by the number of zeros that follow the digit, in reverse order. See Martin's solution …

Retina, 47 43 36 0 ! T`p`0`\b(1+)\b(?<=(?=.*1\1).*)|! Try it online! or try all the test cases Thanks to msh210 for golfing 4 bytes! Also big thanks to Martin for 7 bytes! Explanation: 0 ! Re …

Python 2, 31 lambda l:l and l==zip(*zip(*l)) This requires the lists to be lists of tuples. zip Drops extra elements if the input was ragged, so double zipping is only a noop if the lists all have …

Pyth, 5 bytes >E<QE Try it here Takes the arguments in the opposite order. < and > in Pyth trim based on argument order. For example, <Q5 will trim off all values in the input after the fifth one. …

Retina, 17 15 bytes +m`^(.+)¶\1$¶? Try it online! Saved 2 bytes thanks to Neil and Martin! Replaces each pair of numbers with nothing. This process loops until no changes are made.

\d+ $*1; We change the input array of numbers into a semicolon separated unary array, so we'd have: 1; 111111111111111111111; ^ 11@ Put d into our code at the beginning, giving us: 11@1; 111111111111111111111 … We also add a leading a to these numbers, to indicate that something was kept, along with the ; to indicate it should be permanently part of the array. …

Pyth, 8 bytes smLhSdcF Try it online! This answer is mostly straightforward in that c provides the appropriate splitting behaviour. After that, we map twice to each element of the inner list the e …

Then the final "sorting values" array will be [0, 1, 4, 3, 4, 5, 8, 7, 8]. … Thanks to the stable sort, the ties are broken by the order that the values originally appeared, so we get the final array we want. …

Pyth, 8 j0_Mcz\0 Split on zeros, reverse and join back on zeros. Test Suite