The movies. They have their own continuity together, but they're all so strange and don't fit with the rest of the show.
Later seasons had entire seasons' worth of episodes where the hamsters traveled to Lapis and Lazuli's world of candy, though this was dialed back for the final seasons.
Germans Love David Hasselhoff: It was very popular in Italy. Cristina D'Avena, who performed the Italian theme song (of this series and hundreds of other animes) made an album dedicated to Hamtaro in 2003, with 19 songs related to all the protagonists (including a shipping song about the Howdy/Pashmina/Dexter Love Triangle, no less).
Stan has been paired with just about every ham-ham on the show! Yes, including his own twin sister!
Second to Stan is Pashmina. She already has Howdy and Dexter vying for her and Stan also flirts with her quite a bit. She also tends to be the ham-ham choice for Ships That Pass in the Night with ham-hams like Panda being paired with her.
The second season theme is so fast-paced and contains so much ham-speak that it's not unusual for transcriptions of it to often get at least some of the lyrics wrong.
And then there's 200% no Jumon, see Memetic Mutation above. Full of gems like You see the hand with the bomb-candy! and Ninja Dante!
Never Live It Down: Most of the hate for the series in the west purely boils down to the fact that it aired on Toonami once. Even years after it no longer airs on it, it seems to be the only thing people can talk about in regards to the series.
Periphery Demographic: For every preteen kid that decried this show as a sign of Toonami's end times, there was another kid within the same demographic that admitted to liking the show or secretly watched and said nothing for years to keep up with appearances. There were also even those who didn't care a wit about anything else on Toonami who watched the show simply because they liked this type of show and, in some cases, knew some of the voice actors from other series.
The Scrappy: While Lapis and Lazuli have cute designs, most of the show's Seasonal Rot is directly attributed to them and Sweet Paradise to the point that they took over a majority of the show following their first appearances. They had to be dialed back significantly for the show to regain its slice-of-life elements.
Back when this show was on Cartoon Network, you wouldn't believe how many people fought over Hamtaro/Bijou or Boss/Bijou almost to the point of Die for Our Ship in some circles. Dexter/Pashmina and Howdy/Pashmina got this treatment as well.
Some people think Spat, the cats and the chicks are cute/funny. Other thinks they're Premium Grade-A Nightmare Fuel.
The lyrics to Glitter's song "Love is All Around" may count. Kinda understandable since Glitter's music is mostly marketed to preteen girls such as Laura and her friends.
Took the Bad Film Seriously: While it isn't a bad show, putting Hamtaro on Toonami was not one of the network's better ideas; it was completely out of place for the block and almost guaranteed a hatedom from the get-go. So when Executive Meddling gave them the show, the team went completely for broke on the promos, using a Peter Cullen voice-over in a completely serious tone over heroic hamster antics in a valiant attempt to make lemonade out of the lemon they'd been given. The resulting promos were actually pretty awesome, but also had little to do with the majority of the show.
Vindicated by History: The series was always well-received but it caught heat in America from older Toonami fans who wanted action anime, not cute hamsters. However, the eight-and-under crowd loved the show and it was a Pet Fad Starter for hamsters. As time went on, the younger fans that enjoyed the anime grew up and became vocal in their nostalgia. The reception of the series cleared up and it's known as a Toonami classic.
All the names have been changed and although most of the Japanese Holidays and folk tales have been kept, they too had their name changes. Yet, talk to the American fans and most of them will refer to the dub and not the Japanese version.
One episode that featured Kompeito was called "diamonds of sugar" in the dub.
What an Idiot!: In Rainbow Rescue, the Ham-Hams need to get 7 ingredients that correspond to a colour of the rainbow. Boss, naturally, wants an orange when getting an orange ingredient. The problem is that, along the way, Hamtaro gets a carrot, which is also orange-coloured, its description even explicitly saying that the carrot is orange-coloured.
You'd Expect: The Ham-Hams would bring the carrot.