• The code points of the Unicode blocks Box
  Drawing (U+2500 to U+257F) and Block
  Elements (U+2580 to U+259F) cover
  most of your monospace command-line visualization needs.

    ╭───────╮
    │Unicode│
    │rules! │
    ╰┬─────┬╯
  

• U+2E2E REVERSED QUESTION MARK - the “irony
  mark” to express irony/sarcasm. A useful character⸮

• U+D800 to
  U+DFFF - surrogate code points. They are
  only reserved to ease UTF-16
  encoding.

• U+FEFF ZERO WIDTH NO-BREAK SPACE - it’s name
  suggests, that it can be used like U+2060 WORD JOINER. And in fact the
  latter was introduced to inherit its semantics. This is because U+FEFF had
  become a special beacon called the byte order
  mark, that was placed on
  the beginning of some UTF-8 files. In complying software (including many
  text editors) this character is stripped from the start of a file and
  handled as metadata. In non-complying software (like the PHP interpreter)
  this leads to all sorts of fun behaviour.

• U+FFFD REPLACEMENT CHARACTER - when a
  character cannot be displayed (e.g., decoding an erroneous UTF-8 sequency),
  this code point steps into the breach.

• U+1D455 is missing. It would be an italic
  small “h”. It was not encoded, because it would be identical to the Planck
  constant ℎ (U+210E).

• U+FF03 FULLWIDTH NUMBER SIGN - it is the
  "Japanese Hashtag" ＃. Sites like Twitter accept it as equivalent to the
  regular # (U+0023).

• U+202D and
  U+202E - change the text direction.
  Relevant XKCD:

  

• U+FE0E VARIATION SELECTOR-15 - force
  black-&-white emoji. If this code point follows an emoji, an explicit
  monochrome rendering of the emoji is requested (if the client supports it).

• U+FE0F VARIATION SELECTOR-16 - force
  colorful emoji. If this code point follows an emoji, an explicit colorful
  rendering of the emoji is requested (if the client supports it).

• Diacritics and combining marks: There is a host of
  characters, that add
  to the characters before. Those are called Combining Marks. Unicode
  provides a handy FAQ on the
  details, but in a nutshell: If you add one after a character, it is placed
  on top of that previous one. So, a + ̊ = å. This may lead to all kinds
  of funny problems, because for some combinations there are pre-composed
  characters. Our little å here can also be encoded as U+00E5. You might
  note, that while this has a length of one character, the combination of a
  and combining ring has a length of two characters.

  Of course, one can also do fun things with those characters like
  this answer on StackOverflow.

• The Regional Indicator Symbols
  U+1F1E6 to U+1F1FF resemble the 26 latin characters. They are used to
  create flag emoji. Since the Unicode consortium didn’t feel like getting on
  board with international politics, the solution to flags is to combine
  these 26 characters to the respective ISO code for a country. Examples:

  Country	ISO Code	Code Points	Emoji (if supported)
  USA	US	U+1F1FA + U+1F1F8	🇺🇸
  Germany	DE	U+1F1E9 + U+1F1EA	🇩🇪
  China	CN	U+1F1E8 + U+1F1F3	🇨🇳

• Skin color of emoji: There are five code points, that control the skin color
  of emoji, U+1F3FB to U+1F3FF.
  They are called “Emoji Modifier Fitzpatrick Type” 1 to 6, with 1 the palest
  and 6 the darkest. If one of these characters follows an emoji, that emoji
  is meant to be rendered in the appropriate skin color of the Fitzpatrick
  scale. If no such
  modifier is added, the skin tone should be unnatural, e. g., bright yellow.
  Fun fact: Since the Fitzpatrick modifiers are normal code points, emoji
  with such skin colors have the length 2, which Twitter users noticed first.
  Here is a comparison chart directly from the
  specification:

  Code	Name	Samples
  U+1F3FB	EMOJI MODIFIER FITZPATRICK TYPE-1-2
  U+1F3FC	EMOJI MODIFIER FITZPATRICK TYPE-3
  U+1F3FD	EMOJI MODIFIER FITZPATRICK TYPE-4
  U+1F3FE	EMOJI MODIFIER FITZPATRICK TYPE-5
  U+1F3FF	EMOJI MODIFIER FITZPATRICK TYPE-6

• U+00A0 NO-BREAK SPACE - force adjacent
  characters to stick together. Well known as   in HTML.
• U+00AD SOFT HYPHEN - (in HTML: ­)
  like ZERO WIDTH SPACE, but show a hyphen if (and only if) a break occurs.
• U+200B ZERO WIDTH SPACE - the inverse to
  U+00A0: create no space, but allow word breaking.
• U+200D ZERO WIDTH JOINER - force adjacent
  characters to be joined together (e.g., arabic characters or supported
  emoji). Apple uses this to compose some emoji like different families.
• U+2060 WORD JOINER - the same as
  U+00A0, but completely invisible. Good for writing @font-face on Twitter.

For better comparison of which code point has which effect, consult this
table:

Smashing Magazine featured a comprehensive
article on the
different types of whitespace.

• U+0000 <control> - first code point.
• U+10FFFF (non-character) - last code
  point. The whole rest of its plane apart from U+10FFFE, the code points
  in the 0x10000-0x10FFFD range, are private use characters, guaranteed to
  be never filled by a future Unicode standard.
• U+1F402 OX - shortest name.
• U+1FBA8 BOX DRAWINGS LIGHT DIAGONAL UPPER CENTRE TO MIDDLE LEFT AND MIDDLE RIGHT TO LOWER CENTRE
  and
  U+1FBA9 BOX DRAWINGS LIGHT DIAGONAL UPPER CENTRE TO MIDDLE RIGHT AND MIDDLE LEFT TO LOWER CENTRE - longest name: 88
  characters each.
• U+FDFA ARABIC LIGATURE SALLALLAHOU ALAYHE
  WASALLAM - longest decomposition form: 18 characters.
• U+5146 and
  U+16B61 - code points that represent the
  highest “single-digit” number. In both cases that’s 1,000,000,000,000, a
  trillion.
• U+0F33 TIBETAN DIGIT HALF ZERO - code point that
  represents the lowest “single-digit” number and at the same time the
  only negative one, -½.
• The trophy for most useless code points goes to
  U+0080,
  U+0081 and
  U+0099. These so-called C1 control
  characters are more or less unspecified. They got into Unicode, because
  they were present in the very first version of what should later become ISO
  10646, the ISO-standardized version of Unicode. They were meant to be part
  of an upgrade to ISO
  2022, that
  never came to be.
• A close second place in this regard goes to the CJK unified ideographs
  妛,
  挧,
  暃,
  椦,
  槞,
  蟐,
  袮,
  閠,
  駲,
  墸,
  壥, and
  彁. These so-called “ghost characters”
  came to Unicode via the Japanese JIS standard, where they were added, because
  they were mis-read or misinterpreted from other signs, when JIS was compiled
  from original printed text sources.
• U+006F LATIN SMALL LETTER O - leads the list
  of characters with confusable shapes. Of all the possible mappings in the
  list of confusable
  characters, the small “o”
  leads with a whopping 73 entries of similar looking glyphs, followed by
  U+006C LATIN SMALL LETTER L with 70
  entries.
• U+1F4C0 DVD - only code point name without any vowel (source)
• U+3106C CJK UNIFIED IDEOGRAPH 3106C - the
  character with the most
  strokes: 84.
  Take your time to write this one!

• U+1680 OGHAM SPACE MARK - a space that looks
  like a dash. Great to bring programmers close to madness: 1 +  2 === 3.
• U+037E GREEK QUESTION MARK - a look-alike to
  the semicolon. Also a fun way to annoy developers.
• U+1DD2 COMBINING US ABOVE - this is the most
  romantic code point.
• U+F8FF PRIVATE USE CODEPOINT - this private
  use code point is rendered as Apple logo on many Apple devices.
• U+1F574 MAN IN BUSINESS SUIT LEVITATING -
  A rather curious character, that only made it into Unicode for its
  appearance in the Webdings font (for reasons of backwards compatibility).
• U+1F596 RAISED HAND WITH PART BETWEEN
  MIDDLE AND RING FINGERS - the Vulcan salute. Live long and prosper!
  🖖
• U+1F918 SIGN OF THE HORNS - Rock on!
  🤘
• U+2800 BRAILLE PATTERN BLANK - A Braille pattern that has zero of its six or eight dots filled in. According to the standard: “* while this character is imaged as a fixed-width blank in many fonts, it does not act as a space” Essentially it is rendered as white-space, but since it is designated as not white-space it isn't matched by white-space-validating regular expressions. This can be used to bypass all kinds of validation that disallows or trims white-space.

For plain-text gaming, Unicode is well equipped with several complete sets:

• Chess figures.
• Card suits and even a whole deck of
  cards complete with joker and back
  of card.
• Die faces and a nice die
  emoji.
• Go pieces.
• Draughts (or checkers) pieces.
• Shogi pieces, a
  Japanese variant of chess.
• Domino tiles
• Mahjong tiles

• Cross-platform terminal characters - a list of characters that work on most terminals.