Exploded view of a string

Python 3.5+, 77 46 44 41 bytes

lambda s:[a*s.count(a)for a in{*s}-{' '}]

Pretty simple. Goes through the unique characters in the string by converting it to a set (using Python 3.5's extended iterable unpacking), then uses a list comprehension to construct the exploded diagrams by counting the number of times each character occurs in the string with str.count. We filter out spaces by removing them from the set.

The order of the output may vary from run to run; sets are unordered, so the order in which their items are processed, and thus this answer outputs, cannot be guaranteed.

This is a lambda expression; to use it, prefix lambda with f=.

Try it on Ideone! Ideone uses Python 3.4, which isn't sufficient.

Usage example:

>>> f=lambda s:[a*s.count(a)for a in{*s}-{' '}]
>>> f('Ah, abracadabra!')
[',', 'A', 'aaaaa', 'd', '!', 'bb', 'h', 'c', 'rr']

Saved 3 bytes thanks to @shooqie!

Jelly, 5 bytes

ḟ⁶ṢŒg

Try it online!

It does return an array, just that when it is printed to STDOUT, the separator is gone.

This is indeed a function that can be called as such (in Jelly, each line is a function).

ḟ⁶ṢŒg
ḟ⁶      filter out spaces
  Ṣ     sort
   Œg   group

Retina, 13 bytes

O`.
!`(\S)\1*

The sorting is very easy (it's a builtin), it's separating the letters that takes 9 bytes. Try it online!

The first line sOrts all matches of the regex . (which is every character), giving us !,Aaaaaabbcdhrr.

Match is the default stage for the last line of a program, and ! makes it print a linefeed-separated list of matches of the regex. The regex looks for one or more instances of a non-space character in a row.