I have a Kenwood TM-261. It has the frequencies from 118 to 173 MHz. What frequencies can I transmit on without a licence?
None. Basically, aside from a few ISM bands, none of which are covered by your radio, you can transmit nowhere without a license, unless you're using hardware that restricts you to legal usage (e.g. DECT phones; you don't need a license to operate a wireless indoor phone, but the phone has to be built in a way that prohibits any other usage).
In addition to the answer from @Marcus, I'd like to point out that (since you already have the radio) it's just a small step to get a basic ham radio license. Not familiar with the classes as used in Canada, but surely there is a "basic" class which shouldn't take too much effort to get. While pretty basic, the knowledge required is rather interesting (basic propagation, transmission and technical/electronic knowledge as well as common radio operator do's and don't and practices). It's likely rather cheap as well. It will get you your own call sign and privileges to transmit and have conversations on a couple of bands, one which is the 2-meter band around 145 MHz which you can do with your radio. Add a cheap SDR dongle and some wire to receive and you could just as well contact and talk with/over the international space station. Just in case you have the idea that the "average" radio operators are not the kind of group you relate to (I had that idea), you might be right. HOWEVER: the last few years, an amazing amount of new possibilities have come up, leading to a whole new group of amateurs doing really cool things with new technology. Just take a look at https://hackaday.com/?s=Radio to get an idea...