Badfinger - Wish You Were Here is their only album I love, and I think sufficiently fits the genre definitions.
Posies - I never know whether I really like them or not. I think Frosting On The Beater is their best, although Dear 23 is maybe more purely power pop.
The Raspberries - they're a key player in this genre so should probably be included, but I don't know their albums at all. I think "Go All The Way" and "Overnight Sensation" are their two classics so I'd pick one of those two albums - seems like people think the last is the best.
Flamin' Groovies - Teenage Head is a good album too but is much more in the Stones vein than the power pop vein, so I wouldn't include that.
Cheap Trick - I think Budokan might be my pick but you can't go wrong with any of their first few studio albums.
New Pornographers - borderline I think, but Twin Cinema is close enough to count - I'm less convinced on the two earlier albums.
Some other acts to consider:
Game Theory - maybe they're a little more college-rock, but I think they count. Big Shot Chronicles would probably be my pick (I like Lolita Nation more but it's a little too weird for these purposes).
Guided By Voices - Isolation Drills qualifies I think if their more well-known albums don't. Is it a seminal album in the genre? Probably not I guess.
Let's Active - Big Plans For Everybody. Probably don't need this if you have the Game Theory since they sound fairly similar.
The Searchers - Searchers. Their "comeback" album, very solid. And seems a fitting inclusion since they kind of invented the genre with "Needles and Pins".
The Hollies, The Byrds, The Move, The Nazz. Could argue for them as precursors for the genre if you want.
The Nerves - s/t. Just an EP but a cult favorite that was covered by Blondie.
Squeeze - I don't love any of their albums but Singles - 45s and Under is a great comp.
The Pursuit Of Happiness - Love Junk.
Tommy Keene - Songs From The Film.
Some more borderline picks:
Soft Boys - Underwater Moonlight/Robyn Hitchcock - Fegmania. I dunno if these count but they're in the ballpark.
The Undertones - another borderline band but I think some people would include them. I don't really like them so I don't know which albums are supposed to be good.
Material Issue - Freak City Soundtrack (or maybe their debut, but I don't think I've heard that one).
The Lemonheads - It's A Shame About Ray
The Replacements - Let It Be
Lastly, power pop is almost definitionally a male genre - at least, fans of the genre seldom consider any female acts to be part of it. I suspect this largely reflects sexism since the genre requirements are otherwise so vague. So I'd be inclined to include at least one of the following, if only to troll the misogynists - but I think they're all good albums that fit the sonic requirements:
The Bangles - All Over The Place
Juliana Hatfield - Hey Babe (or one of the first two Blake Babies albums)
Rilo Kiley - Under the Blacklight
That Dog - Retreat From The Sun, or Old LP
Voice of the Beehive - Let It Bee
Liz Phair - s/t (ok, this would be a very trollish pick)
Kirsty MacColl - Titanic Days
Hole - Celebrity Skin
Blondie - Eat To The Beat
Taylor Swift - Fearless (which just had a high-profile rerecording come out, so it'd be a timely pick!)