PSU's actually "go into "cases. What I think you mean is will the cable ends match ?
Today's MoBo's have more / bigger power connectors than older ones. Back in the day a 20 pin power cable was it. Now most PSU's provide a 20+4 power connector and an 8 pin (or 4+4). If you're components are from different PC "eras", you'll want to confirm that the PSU provides what you need by reading the manuals for both components.
"Does it?" or "Will it?" can be answered mostly in reference to the cable ends, as described above. "Should it?" is another story, and actually the more important one (in my opinion); there are a lot of PSU-shaped objects out there that are hardly safe or stable enough for light bulbs, let alone delicate electronics. The best site I've found for tutorial articles on PSU construction and quality is www.hardwaresecrets.com. If you are interested, you can read a lot there about what distinguishes a good PSU from a bad one. Or, you can read some of their reviews, and see what happens when a bad PSU is expected to output even a fraction of its load. Another great review site (not quite as much technical detail, but humorous yet clear writing) is www.jonnyguru.com.
My own personal rules of thumb are:
1. Use a PSU calculator to obtain an estimate (may be a little high, but that's ok) of how many watts you need.
2. Find a PSU of the appropriate wattage that has full range active PFC (no little voltage switch) and is 80+ certified for efficiency.
The latter assures you will have a PSU of a reasonably modern design, with most of its wattage on the +12V rail(s) where it is needed by a modern PC, that can actually output what's on it's label (although the testing is done in an unrealistically cool environment, the PSU is given time to warm up), and do so efficiently.
3. If at all possible, the PSU has at least one positive competent technical review, i.e. one with load testing, waveform analysis, etc; I'll go lax on #3 if the brand is otherwise exemplary, like Antec, Corsair, or Seasonic.