I will group the options based on output. Assume the following vector for all the examples.
v <- c('z', 'a','b','a','e')
For checking presence:
%in%
> 'a' %in% v
[1] TRUE
any()
> any('a'==v)
[1] TRUE
is.element()
> is.element('a', v)
[1] TRUE
For finding first occurance:
match()
> match('a', v)
[1] 2
For finding all occurances as vector of indices:
which()
> which('a' == v)
[1] 2 4
For finding all occurances as logical vector:
==
> 'a' == v
[1] FALSE TRUE FALSE TRUE FALSE
Edit: Removing grep() and grepl() from the list for reason mentioned in comments