Is it nowadays a full equivalent of the term "spouse"? Or does "partner" imply that the couple in question isn't formally married?
Also is "partner" more often used by or about same-sex couples?
Update: You have been very helpful, I love you, fellow linguaphiles! And now I'll confess that I become interested in the term after watching the new "Sherlock" series.
So the verdict is that "partners" is more often used about same-sex or other nonheteronormative couples or heterosexual unmarried couples, but it usually implies a long-term commitment. And also it's a handy way to avoid undesirable labels or lengthy explanations.
But the meaning seems to be in transition and also depends of the country, so please read all the comments to get the full picture.