On 2013–09–21 Xan wrote:

> \diameter produces a diameter symbol. What is the equivalent in ConTeXt?

  ⌀ or \varnothing

Have a look at char-def.lua for a list of context names for various
glyphs. It might make sense to enable the fonts.missing tracker.
Then ConTeXt warns you that a particular glyph is not available.

  \enabletrackers [fonts.missing]

> Is there any compilation of symbols avaliable in ConTeXt?

Not that I'm aware of. In ConTeXt you have easy access to all
characters of any font¹. Either input the character directly if it's
present in the current font or you can create a symbol:

\definefontsynonym
  [minion]
  [name:minionproregular]

\definesymbol
  [leaf]
  [\getnamedglyphdirect
    {minion}
    {bullet.010}]

\starttext
  Foo \symbol[leaf] Bar
\stoptext

Marco

¹ http://tex.stackexchange.com/a/87563/5245