A rather difficult client of mine is demanding that I make amendments/bug fixes to websites that I delivered to him at times ranging from 2 to 8 months ago.
Unfortunately, there is no written contract in place.
Do I have any legal obligation to satisfy this difficult client? (I am in Canada).
I am with Sagewing, however I would also like to know what kind of bugs are being reported. Are these general defects in the code which existed during production yet you failed to pick up upon or are they the result of “wear” (such as something that occurred recently which altered the compatibility or something the end user broke). My advice would be to examine each bug on a case by case basis, decide how long it would take to fix, whether you are responsible for the defect and if your verbal agreement (to undertake work) - or written if via email included such issues in the guarantees you gave to the client. As you don’t appear to like this client very much I would say that unless the bug contradicts what you said you would do, simply tell him that you’re not responsible for issues which have come to fruition post the works termination and any defects should have been declared before the working period was extinguished. Saying that they accepted the work in the condition it was in is legally binding and while some errors may exist (if their ones you feel you can’t have for-seen or controlled) you will be required to charge a fee to have new issues resolved that extend beyond your obligated working period (though let it be known here and now I’m not a lawyer!). 
The question that comes to my mind is, ‘why WOULD you provide services to this client?’. Do you have any obligation to the client, written or verbal? Did you make any representations to the client that you would provide ongoing services, or did you promise to provide services that haven’t been provided yet?
The fact that you don’t have a written contract probably doesn’t matter. You can still have a verbal contract, or you may have no agreement at all. What matters most is if some obligation exists, regardless of how the agreement is made.
So - why would you possibly owe this client anything? From what you wrote, it sounds like you provided services for the client in the recent past and presumably got paid for it. You also tried to terminate the relationship. So, unless you promised something to the client and didn’t provide it you probably don’t owe anything.
If the client suddenly has decided that the services that were provided aren’t up to his satisfaction level, that is really subjective and it’s doubtful that he can obligate you do to more. That is, unless you actually didn’t provide the services in an industry standard manner or in to the quality that was promised.
With regard to amendments, I’d personally say no.
With regard to bug fixes, I’d personally say yes, but you might want to read this thread, which discusses that exact question
I would say that your previous pricing was based on time worked, and you would be happy to make improvements or solve bugs, but you will need to bill at your normal hourly rate. ALL SOFTWARE contains bugs. Now if you made a really stupid mistake and it takes you only a short time to solve it, you might want to do this as a token of good will.
I’m not really interested in expressing good will to this client I’m afraid. In fact the reason he is now demanding this work is that I had previously informed him that I would no longer be accepting projects from him (because he is too difficult and too cheap - though obviously I didn’t tell him that!).
He didn’t take kindly to this news, hence the disgruntled reaction. He is even implying he will take legal action if I don’t do everything he asks to his ‘satisfaction’.
As you can imagine, I would like to extricate myself from all involvement with this client with minimum fuss and maximum speed.