Like Rog says, Picasa installed on your PC will still work OK but won't get any more development. By the sound of it, it works well enough as it is and any 'improvements' they might've made in future would likely just be bells and whistles you don't need /won't use. E.g. MS Office 2003 still functions OK.
Way I read it, if you use Picasa Web Album all your pics will automatically be copied to the new(-ish)
Google Photos - *might* be worth giving it a try.
Although it does seems very good, Picasa isn't something I've used much so I can't say what might be a good alternative, possibly something mentioned here:
Best Free Digital Photo Organizer or
Best Free Digital Image Viewer.
I've used DigiKam, IrfanView, XnView, Faststone and they're OK, just depends what you're looking for. Don't think any of these have Web Albums, though.
Might be worth seeing what Google say, and keeping an eye on there for new developments:
Picasa blog