Is it still possible to get Apple's iPhoto app for OSX?

If you owned it before, it may be available via download. You may be able to purchase the the DVD version from Amazon or elsewhere.

That said, Apple most likely won't update it for support beyond El Capitan. You should look at either Photos (which isn't half bad - and made better using Extensions) or something else.

 

OP:

What version of the OS are you using now?
Do you have iPhoto up-and-running now?

The final version of iPhoto is 9.6.1.
The way to get it is:
1. delete your existing copy of iPhoto from the applications folder (put a backup copy somewhere else)
2. go to the App Store, click on "purchased items", iPhoto should be there (even though previous version may have been free)
3. download it (again). You should receive version 9.6.1.

Having said that, there are -other ways- to get 9.6.1, although the sources may be "non-approved". It -can- be found, if you look for it...

 

Doesn't appear in my Purchases.

 

Still shows in my purchases, not sure why since Apple does not support it. But I have to agree that you should really go with something else.

 

That is assuming 1. OP doesn't need any features that Photos lacks and 2. developers write enough extensions, currently the number is quite small.

OP:

What kind of needs do you have, are you using only some of the features in iPhoto or all of them?