As my Master said, we can pay our respects to our
ancestors.
It doesn't even have to be your direct family's ancestors, but
anyone who has done great deeds, deserved to be respected, etc...
you can pay your reverence and respects to them.
This is NOT about worshipping them, and not about asking for
favour... this is about paying our respect and remembrance of these
people for their noble deeds.
Of course though, we should not pay reverence or honour the evil,
criminals, murderers, and so on that has harmed others...
Praying to the dead will *not* make them suffer less in their
afterlife... depending on their karma, they may be reborn in higher
realms like celestial or human realm, or the lower realms.
However, nothing can benefit them (whether offerings, burning paper
money, or praying) in their afterlife... the only way we can
benefit them is to dedicate merits to them. Also see: http://www.jenchen.org.sg/vol5no1a.htm
As for praying to our ancestors for favours, honestly speaking, it
doesn't work this way. Because if our ancestors have been reborn in
higher realms or human realm... it is already a different
lifetime.. they have moved on. Similar goes to being reborn in
lower realms like hell or animal realms...
If your ancestor has turned into a ghost, he himself is undergoing
suffering in the ghost realm... so how can he possibly give you
much blessing when he himself does not have much blessing?
So, it is advisable not to be too superstitious over these
things.
We can pay our respect to ancestors, but it is not really good to
be superstitious or dependent.
Update: sorry, just realised you meant 'do THEY get blessings'...
but anyway I have replied above. Anyway it strikes me as kind of
strange, because usually people pray to them TO get blessings for
himself... how would praying TO them make THEM get blessings? "I
pray to you to bless yourself." 
doesn't make much logical sense to me.
