You can also tweak your Coalesced with the Coalesced Editor to take screens using the game alone. (Back up your Coalesced.bin before you do anything with it. Also be aware that some changes might get you banned from multiplayer.) I'm not sure about the exact bindings needed as I use Fraps myself, but there are tutorials explaining how it works around. Let's see...
The binding should be:
( Name="F8", Command="Screenshot" )
You can replace F8 with the key you wish. Just make sure it's not already in use.
(Also, I don't recommend deleting lines. ANY lines. Not even the ones you have added. The editor somehow fails to process it and I've had a lot of trouble with it - the game would not even start, telling me it's not responding.)
When you open the Coalesced.bin in the Editor, navigate to bioinput.ini > sfxgame. Personally, I would add the binding to sfxgamemodebase, sfxgamemodecinematic, sfxgamemodeconversation, sfxgamemodedefault, sfxgamemodedreamsequence, sfxgamemodemovie. (You can use the same key in all of them.)
I do not know whether they're all necessary, but sometimes when you only make a change to, say, sfxgamemodebase, it might not work during cutscenes and such.
Personally, I've been using Fraps and saving images in BMP, then converting them to PNG, and it's been working perfectly for me. I understand if you have a different experience, though. I have a friend whose Fraps tends to act up, too.
Hope I'm not redundant, looking at all the answers.
EDIT: I'm not sure where the screenshots will go with ME3. I remember once doing these tweaks for ME2 and I thought it didn't work because my Documents\BioWare\Mass Effect 2\ScreenShots was empty, only to find out much later that there's another folder in Documents\BioWare\Mass Effect 2\BIOGame\Screenshots. So I recommend checking twice before dismissing the changes as failures and then finding 20 GB folder with pictures later like me. 