Depends entirely on where you are travelling. For many parts of the world, including most of Europe, you really should stick a Canadian patch on your jacket, or similar. When I spent a year backpacking around Europe, I found (as an Australian) that Americans were basically the running jokes of the backpacker scene, and in some countries the locals loathed them as well. Often that wasn't entirely fair - the cliched 'ignorant American' isn't likely to show up in a backpackers' working the bar in rural Spain - but by and large the typical US tourist is seen to rush in and out of a country in a generic packaged tour, with no knowledge of local languages/culture and very little comprehension of the world outside the US. It's a hard reputation to shake, even for the Americans who are multilingual and well-educated (though admittedly, even then most Americans I ran into were more ignorant about other countries than most people of a similar educational sophistication).
Obviously if you're doing the 'fly-in/do-a-tour/fly-out' kind of trip then you aren't going to have to worry about the backpackers' scene. BUT still pack the canadian patches if you are spending a lot of time in France, Germany, Sweden, Italy or Spain. The last two aren't as anti-American, so long as you act appropriately to the culture. Big mistake that you see Americans making there is to go into a shop and expect to be 'the boss' or for there to be a 'customer is always right' attitude. In Spain and southern Italy, if you go into someone's shop, the onus of politeness is revesed - it's THEIR place, so you need to be polite to them. People are used to having things move at a slower pace, so cafe/shop staff will take their time with serving you, and won't hesitate to fire back at you, or just refuse to serve you, if you complain in a manner they feel is unreasonable. I've seen Americans in Spanish shops be denied service because they've started tapping their fingers on the counter impatiently - the staff won't tell them to get out, but they'll just ignore them and serve everybody else until the finger-tapper gets the message. Most of the time they'd probably put up with it from other locals, but again...Americans come with a reputation.
From personal experience, in France you want to make clear to pretty much everyone that you're not American or English. E.g. when I asked when the next train to Lyons is that day, the rail guy says 'I do not speak english, no trains today'. I then say 'Je ne suis pax American! Je suis Australian!' (bad French for 'I am not American! I am Australian!'. Rail guy (in English): Oh, I'm sorry. There are trains leaving from here to Lyon every 2 hours on track number 4. Do you want to reserve a ticket?'
That kind of thing happened a lot, and friends who have been to France have had similar experiences (same for other European countries, but France is reknowned for it) - locals would be deliberately difficult/rude if they thought I was from the US, but would happily speak english and help out once they knew I wasn't American.
As a consequence, every single Canadian I met while travelling (and I met a lot) had the flag on their luggage and on at least one item of clothing that they'd be wearing often (say a hat, or a jacket). This included several Canadians who started off travelling without the flag anywhere, but who had quickly purchased and attached it after discovering the anti-Americanism, and the comparative popularity of Canadians.
In Australia, Canadians are much more well liked than Americans, but people aren't going to personally dislike you or hassle you about it one way or the other.
TL;DR: Canadians are well liked in Europe, Anti-Americanism is common in Europe.