Remember Me - S4-E5
Trivia: Gates McFadden (Commander Beverly Crusher, M.D) did all of her own stunts in this episode, while she was early on in her pregnancy.
Half a Life - S4-E22
Trivia: One of the computer readouts that Dr. Timicin studies in Engineering has the numeric code "4077". This is a reference to David Ogden Stiers' earlier role on the series M*A*S*H.
The Best of Both Worlds (2) - S4-E1
Trivia: When the Enterprise is travelling through the debris field, one of parts it goes past resembles the secondary, or bottom part, of the Enterprise A.
Answer: He brought the Borg to the Alpha Quadrant and showed them that it was full of worlds waiting to be assimilated. Guinan's homeworld was their first stop, and they assimilated everyone and took over the planet, leaving The Survivors of her race without a home. Q is ultimately responsible for that.
Captain Defenestrator
By the time Q takes the Enterprise to meet the Borg, Guinan already knew who they were and they had already destroyed her world. Therefore the above answer can not be right. I believe Guinan is much more than she appears, and her people have had encounters with the Q in the past. It is these interactions, that obviously were not pleasant, that fuels her distrust.
oldbaldyone
That's what the above answer is saying. Q brought the Borg to the Alpha Quadrant (not Earth) and the Borg destroyed Guinan's home world in the late 2200's, which is why she hates Q. Although she met Q in 2160 and they both saw each other as enemies right away.
Bishop73