My best guess would be Hyperion and The Fall of Hyperion by Dan Simmons, if your "spacegates" were called farcasters in the book.
scifi.stackexchange.com/users/23/Mike Scott
Harry Harrison's "One Step From Earth" is a collection of short stories exploring the discovery and use of a "portal system".
While the first story is more "hard" in trying to explain the uses of the technology, the remain eight are more "soft" and concerned with how the technology changes society and people.
I distinctly remember a man fleeing from a crime he had just committed, skipping across many worlds in an attempt to lose his persuer.
scifi.stackexchange.com/users/9302/Jim Green
Probably not what you are thinking of, but in the Ringworld books, the Puppeteers used teleporters called 'stepping discs' - you step onto it and it teleported you to another location.
They seemed to be mostly for local use, though.
scifi.stackexchange.com/users/26/Michael Kohne
Pandora's Star by Peter.
F. Hamilton uses portal technology to step between worlds, but the general application was Train stations, not individual rooms.
But it is a good example of this technological mechanic.
http://en.wikipedia.org/wiki/Commonwealth_Saga
scifi.stackexchange.com/users/9255/Jared Tritsch
I seem to remember a similar technology being used in The Dosadi Experiment by Frank Herbert, I'm not sure if it was used in the book before it, Whipping Star.
scifi.stackexchange.com/users/140/Amos
There is a similar mechanism, initially presented as a natural phenomenon but later revealed to be perhaps technological in origin, in Doris Piserchia's "Spaceling".
It's not the book you're thinking of, in part because the portals drift and can be unpredictable, but if you're interested in the theme you may like it.
scifi.stackexchange.com/users/17317/Michael Stern
If memory serves, the James H. Schmitz Telzey Amberdon story "The Lion Game" has a world where most "buildings" are actually groups of rooms in various locations connected by portals and are not actual buildings as we know them.
The heroine ends up trapped in a hotel called the Luraal where some of the portals are traps.
She is trying to deal with hostile aliens and escape the building.
scifi.stackexchange.com/users/63996/zeta-band
I am trying to identify the name of a book that involved a civilization that utilized spacegates to instantly travel across space, literally stepping from one world to another. In the book, a family home could have different rooms located throughout the galaxy and the people simply walked through the doorway to move from room to room (and planet to planet)
Book has spacegates that a person can walk across
scifi.stackexchange.com
<story-identification><novel>
scifi.stackexchange.com/questions/4319
scifi.stackexchange.com/users/2303/Stu
This may be "Hyperion"  and  "The Fall of Hyperion"  by Dan Simmons. Other suggestions include Harry Harrison's  "One Step From Earth"; "The Dosadi Experiment"by Frank Herbert;  Doris Piserchia's "Spaceling"; or the James H. Schmitz Telzey Amberdon story "The Lion Game". A number of books seem to fit the bill as having spacegates in the story. These include Hyperion, One Step from Earth, The Dosadi Experiment and The Lion Game.
A number of books seem to fit the bill as having spacegates in the story. These include Hyperion, One Step from Earth, The Dosadi Experiment and The Lion Game.