Does Springfield still exist in the Futurama future? I don't expect to see the characters travel to the future, but if Fry's descendant could survive, so could the Simpsons.
In the episode "A Big Piece of Garbage" Fry finds a pile of Bart Simpson dolls and he comments about them as if he is aware that "The Simpsons" is a TV show. Also in the episode "Mars University" you can see Simpson dolls hanging in one of the booths when Fry has his flashback to the carnival. These seem to indicate that The Simpsons is a show in the Futurama universe, and not a real place. In the crossover books w/ the Simpsons the Futurama cast gets projected into Simpsons merchandise and the creator states in the foreword that The Simpsons is a fictional TV show in the Futurama universe.
Oddly enough, Futurama merchandise shows up in The Simpsons indicating it's a show in that universe. When Bender showed up in The Simpsons they went through a dimensional gateway, indicating that it's not the same universe.
I agree with Andres that they do not exist in the same universe. In
A Big Piece of Garbage there are Bart Simpson dolls as an indicator of 20th century culture(specifically 20th century not 21st century). This means that
The Simpsons are a TV show in the
Futurama universe just as they are in ours.
Actually, in the audio commentary for I believe Mars University (it has been a long time since I've watched early eps) Matt Groening explains alongside David Cohen that the Simpsons is technically "fake" while Futurama is "real" as in multiple episodes, you see Simpsons characters as stuffed dolls.
Originally, the character designs for all humans for Futurama were also going to have 5 fingers, but in the end, it was harder to animate, and looked strange.
So no, in the world of Futurama (read: our world) the Simpsons, and the town of Springfield are fictitious.
Note that Springfield is referenced in The Simpsons as being in all the states that there is actually a Springfield (as a running gag). So, if The Simpsons is just a show in Futurama, then it is likely that there are just as many Springfields as there are in our time. But there hasn't been any reference to any of them in Futurama so far.
I don't think the Springfield from the Simpsons TV show exists in Futurama's future at all.
Why? Because I don't think the Simpsons and Futurama exist in the same universe at all. In The Simpsons' world, people are yellow. In Futurama, they aren't. Of course, that doesn't preclude some tongue-in-cheek TV show reference ;)