If I have a hard drive that is partioned into 2 parts C for Windows and D for storage and my hard drive crashes would I still be able to access my D drive to get my files off it?

I was thinking yes as long as I install it in another computer and use it as a secondary drive.

That is a big NO!

A hard drive crash affects the entire device including all partitions.

You need to use 2 hard drives for this. To be even more secure, the D: drive should be mirrored.

The ideal combo for light backup is 2 drives as a mirror, partitioned in a C; and D:. If one drive dies, the other has a full copy of the C and D.

Another solution is to copy the D to an external USB or e-SATA drive. The problem is that most people do not do that often enough to make it reliable.

The partitions are just like chapters in a book. If the book becomes unreadable for whatever reason (pages strangely glued together, got thrown into a lake, set on fire, etc) then you can't read any of it.
With different drives, you are hoping that only one will fail at a time, so you still have the other one.
As mentioned below, mirrored drives are the easiest automatic backup (you essentially have two drives, both used identically when you save files).
However, regular backups to DVDs, external drives, etc should be more than adequate unless you are running a data server or and important business database, etc.

Remember though that ALL mirrored drives do is protect from a failure of ONE drive. They do NOT provide any form of backup; once a file is deleted, changed, or corrupted it is in that state on BOTH drives.

I guess two drives it is then :)

To answer your original question, yes.
"HD crash" is somewhat ambiguous.

Of all the "crashes" I've experienced, windows (or my overzealous tweaking) was at fault 90% of the time and only needed to be repaired. This would be a system software crash, and all other partitions are safe enough.
The other side of the coin is a hardware failure where your drive is as useless as a 10yr old calendar. This is what the fine fellows above with their two drives
solution, are protecting against. And yes, it happens.

If you only have the one drive, then yes partition it.

If I have a hard drive that is partioned into 2 parts C for Windows and D for storage and my hard drive crashes would I still be able to access my D drive to get my files off it?
If the C drive simply becomes unbootable due to a software error, yes. If the drive itself fails, probably not. As mentioned, it's best to make backups to an external USB or network drive. Use disk image software for the C drive. Either disk image or file based backup software can be used for the D drive.