Yes, I believe they face discrimination. Gypsi itself is a racial slur, as the group of people are actually called the Romani people. People have stereotypes about the Romani already fixed in their minds, when the Romani are just misunderstood. They are discriminated against by people who call them child stealers, thieves in general, and more. So yes, I believe that the Romani as a race are discriminated against.
The Gypsies have always led a somewhat nomadic existence, without permanent homes or traditional jobs to tie them down. They have been relegated to the bottom rung of the social ladder since the 16th century when they traveled across the countryside in wagons. Still today they are forced to live in squalor, without decent jobs or schools. The Gypsies are the quintessential "downtrodden" race.
Gypsies have been portrayed in certain ways for centuries in literature and more recently in other media. These portrayals create sterotypes, these sterotypes can additionally spread by word of mouth. When you judge people by sterotypes then discrimination follows. Being somewhat nomadic and not having established local roots would further lead to mistrust and discrimination.
I do not think that Gypsies are seen very well in the eyes of others and people often discriminate against them and hold them to a harsher judgment than they might for other people. People assume all of them are only good at stealing and do not care about anything else, and that is not right.
Gypsies as a race are generally not discriminated against in Europe. People have a problem with the thieving and taking of welfare benefits from country natives. When times are tight, as they are now in many parts of Europe, people will try to distinguish who is using up resources, and many of them tend to be gypsies. Those are numbers, not discrimination.