I was consulting the Vatican’s “Ecumenical Directory” today (= directives, save this link in case you have trouble sleeping one night), and came across this paragraph which answers our question: May non-Catholic Christians receive blessings?
121. Blessings ordinarily given for the benefit of Catholics may also be given to other Christians who request them, according to the nature and object of the blessing. Public prayer for other Christians, living or dead, and for the needs and intentions of other Churches and ecclesial Communities and their spiritual heads may be offered during the litanies and other invocations of a liturgical service, but not during the Eucharistic Anaphora. Ancient Christian liturgical and ecclesiological tradition permits the specific mention in the Eucharistic Anaphora only of the names of persons who are in full communion with the Church celebrating the Eucharist.
There are some restrictions and also ambiguities (probably deliberate) in this directive, but the short answer is: Yes, non-Catholic Christians may (generally) receive blessings. It is also important to note that this directive extends to objects as well – so, for instance, a non-Catholic Christian could request that a Catholic priest bless his home. And I have done this on a few occasions. As someone recently said somewhere (maybe I read it on Facebook or Twitter), non-Catholics often believe in the Catholic Church when it comes to dealing with the forces of evil! It’s not uncommon for a Protestant to request holy water or a house blessing if they notice strange phenomena happening in their home.
A few notes about this paragraph: it restricts blessings to Christians – i.e., those baptized with the standard trinitarian formula). Obviously, when a priest (or the pope, as above) is blessing a crowd of people, he doesn’t necessarily know the faith of all present. But he gives the blessing anyway – even if there should be some hindus or muslims or non-baptized atheists present. So this doesn’t have to with crowd circumstances. It is understood that it concerns individual requests for blessings.
It also directs that in the Eucharistic prayer, where – depending on which prayer is used – it is possible to insert names (for example, the memorial of the living, or the memorial of the deceased), only the names of Catholics may be inserted. Finally, please note that this does not have to do with the intention for which Mass is offered – so if you wanted to have a Mass said for a deceased non-Catholic Christian relative, you could.