Mostly known for Progressive Rock.
But all I remember they did or tried to experiment with these genres are: Psychedelic rock (Barrett Era and the Era of Progressive Experiments), Progressive rock, Experimental rock, Post-Prog, Experimental music, Alternative, Space rock, Folk, Avantgarde rock, they tried some of Jazz, Blues-rock (The Dogs Of War for example), Blues (Seamus).
But their music can be classified as blues-based progressive rock which you can clearly hear in songs like Pigs (Three Different Ones), Sheep, It's What We Do or even Shine On You Crazy Diamond (Parts 1-5) and Shine On You Crazy Diamond (Parts 6-9).