Array include any value from another array?

How about Enumerable#any?

>> cheeses = %w(chedder stilton brie mozzarella feta haloumi)
=> ["chedder", "stilton", "brie", "mozzarella", "feta", "haloumi"]
>> foods = %w(pizza feta foods bread biscuits yoghurt bacon)
=> ["pizza", "feta", "foods", "bread", "biscuits", "yoghurt", "bacon"]
>> foods.any? {|food| cheeses.include?(food) }
=> true

Benchmark script:

require "benchmark"
N = 1_000_000
puts "ruby version: #{RUBY_VERSION}"

CHEESES = %w(chedder stilton brie mozzarella feta haloumi).freeze
FOODS = %w(pizza feta foods bread biscuits yoghurt bacon).freeze

Benchmark.bm(15) do |b|
  b.report("&, empty?") { N.times { (FOODS & CHEESES).empty? } }
  b.report("any?, include?") { N.times { FOODS.any? {|food| CHEESES.include?(food) } } }
end

Result:

ruby version: 2.1.9
                      user     system      total        real
&, empty?         1.170000   0.000000   1.170000 (  1.172507)
any?, include?    0.660000   0.000000   0.660000 (  0.666015)

(cheeses & foods).empty?

As Marc-André Lafortune said in comments, & works in linear time while any? + include? will be quadratic. For larger sets of data, linear time will be faster. For small data sets, any? + include? may be faster as shown by Lee Jarvis' answer -- probably because & allocates a new Array while another solution does not and works as a simple nested loop to return a boolean.