Is there a list of my owned psn games?

Solution 1:

Yes, there actually is a list with all contents you have ever "purchased" over PSN (for free content, "purchase" means the first time you downloaded it). That list includes content from the PS3 or PS Vita (possibly also PSP), regardless of which system you are currently using to view the list.
Unfortunately, the list isn't very user-friendly; the more you purchased, the more difficult it is to find what you're looking for. It is sorted by date of purchase and it is currently not possible to change the sorting order.

Here's how to view the list (I have German localization, so the options' names are likely not accurate):

PS3:

Launch the store app, then go down to the third-to-last option, called Show downloads.

PS Vita:

Launch the store app, then touch the ... button on the bottom right corner of the screen; touch the second option from the top, called Download List.

PSP:

(I do not own a PSP, so feel free to edit this point)

Any and all content featured on that list may be downloaded again for free. The only limitation is that you can't download PS3 content to the PS Vita (possibly also the PSP), and that PSP content can only be downloaded onto a PS Vita, if that content is also available in the PS Vita store (you can still download the content over a PS3 and transfer it to the Vita, although there is no guarantee that the transfer will actually succeed)

Solution 2:

If you go into the PS store, then go to account -> available downloads. It will list everything you've bought/downloaded previously and have the option to download them again if they aren't already saved to your system.