Does it need an equator-facing roof? No.
Does it help to face the equator? Yes, but probably not as much as most people might think.
Solar panels are surprisingly productive, even if they're not oriented optimally. If your primary goal in installing home solar is a desire to produce renewable energy (for environmental reasons), almost any roof will do, as long as it's not shaded by other buildings or trees. If your goal in installing home solar is purely to save money, then you may care more about the modest losses from suboptimally-oriented panels.
Let's look at a typical plot of solar panel output, as a function of roof orientation (e.g. relative to the equator), and panel tilt (relative to horizontal):
Let's say your panels are tilted 32° from horizontal. The graph shows that you get 100% of the maximum energy production if you point the panels North (this is an Australian chart). But, if you point the panels Northeast or Northwest, at the same tilt angle, you're still easily within the white area indicating 90+% of the maximum energy production of your panels! And even pointing due East or West, the worst possible orientation (‡), you're still producing about 85% of the maximum. That's only a 15% loss, with a "bad" roof orientation!
Optimal Tilt Angle
If you look closely at the graph, you can also see that if you are pointed away from the equator, the optimal tilt angle also changes. For example, on the above chart, if your roof points ENE (about 75°), then you'll get the highest output (90% of the max) with a tilt angle of less than 20°. Pointing at the equator, the optimal tilt angle was about 32°. So, as your roof points away from the equator, a more shallow tilt angle (flat panel) works better.
Here's a table showing similar relative calculations at a variety of Latitudes.
If you really want to get the precise number for your location on Earth, check out the US NREL's PVWatt tool.
- Pick your location on the world map
- Scroll down in the little popup window and select Send to PVWatts
- Pick the Array Tilt (pitch) and Array Azimuth (direction roof points)
- Press Calculate button
- Record the total yearly AC energy (kWh) for this combination
- Go back and change the Array Azimuth for a different roof orientation, and see what the total yearly AC energy is now
Doing this, you can compare the results for the direction (azimuth) your roof points, with the optimum (180° for Northern hemisphere, and 0° for Southern). That will show more precisely how much roof orientation matters.
As I said, it's not that much.
You can perform the same comparison with Array Tilt.
(‡) Technically, East - West is not the worst roof face to pick. You could, for example, pick a North-facing roof in the Northern hemisphere. My friends in California claim that this is somewhat common, as some people will choose to place their solar panels on the side of the roof that faces the street, so they can show off their green-ness, rather than the side of the roof that's most efficient