I'm a Japanese citizen/resident. I use the Visa Waiver program to get into the US which is a green form that gives you a 90 day visa for entry into the US. The US DHS officer will staple the departure card half of the visa form into your passport that they collect when you leave the country.
When I was leaving LA for Toronto a few days ago, the agent looked at the visa and said, "OK. You have a visa and it is valid through your return." She didn't take the card and sent me to a 1 hour wait security screening line... anyway.
I just past through pre-sreening in Toronto on my way to the US. With Canada to US flights, they do customs and immigration when you leave Canada. A US officer frowned when he looked at my passport.
"You need to return this visa waiver when you leave the US."
"The gate agent didn't take it when I left."
"It is YOUR responsibility to return your visa card. The airlines do it out of courtesy to you, but it is YOUR responsibility."
"It is YOUR responsibility. Although it visa SAYS you have 90 days, you must return the card and get a new one each time."
"It is YOUR responsibility, not the gate agent."
(stern look from officer)
"Yes sir.. no sir.. yes sir... OK..."
I've had gate agents not take my card when I exited in the past. I don't know what the penalty is, but for anyone traveling on Air Canada to Canada from the US. If they don't take your thingie from your passport, I recommend you insist that they do.
UPDATE: Although... according to the FAQ it says that you can travel and come back when you are on the Visa Waiver Program to Canada or Mexico. So if you have to give your stub back, I wonder what you give back when you're leaving the second time. I doesn't say. Hmm...
Q: Can a VWP applicant for Admission Be Readmitted To the United States Follwing a Short Trip To an Adjacent Island, Canada, or Mexico?
* Generally, VWP applicants admitted under the VWP may be readmitted to the United States after a departure to Canada or Mexico or adjacent islands for the balance of their original admission period. This is provided they are otherwise admissible and meet all the conditions of the VWP, with the exception of arrival on a signatory carrier, in which case the inspecting officers have the discretion to grant the applicants entirely new periods of admission.
* The VWP applicant is admissible and may be readmitted to the United States under the VWP after a departure to Canada or Mexico or adjacent islands provided the person:
1. Can identify an authorized period of admission that has not expired,
2. Plans to depart the United States prior to the expiration date of their period of admission,
3. Presents valid, unexpired passports which reflect admission to the United States under the VWP, and
4. Continues to meet all criteria set forth in 8 CFR 217 and section 217 of the Immigration and Nationality Act (Act), with the exception of arrival on a signatory carrier.