Scraping through product pages
There's not a lot to say about such a simple program, mainly nitpicks.

You are violating PEP8 at a few places.
The code reformatted to follow PEP8 would look like this:

def my_crawler(url, max_pages=1, max_items=1):
    for page_number in range(1, max_pages + 1):
        source_code = requests.get(url + str(page_number)).text

        products = SoupStrainer(class_='productTags')
        soup = BeautifulSoup(source_code, 'html.parser', parse_only=products)

        for item_number, a in enumerate(soup.find_all('a')):
            print(str(item_number) + ': ' + a['href'])

            if item_number == max_items - 1:
                break


In particular:


Write method parameters compactly as max_pages=1 instead of max_pages = 1
Break line after :


Instead of range(1, max_pages + 1) I would find range(max_pages) simpler if you only need to do max_pages + 1 in the code. So I'd rewrite the above as:

for page_number in range(max_pages):
    source_code = requests.get(url + str(page_number + 1)).text


And as a mild case of paranoia,
I'd prefer the if statement for breaking out of the loop this way:

if item_number &gt;= max_items - 1:
    break


And yes, it's fine to break out of the loop this way.
I don't think there's a better way.

When you print the item number and the link,
I think this is slightly more readable:

print('{}: {}'.format(item_number, a['href']))


Finally, don't execute code in global scope,
it's recommended to wrap code in an if __name__ == '__name__': guard:

if __name__ == '__name__':
    my_crawler('http://www.thesite.com/productResults.aspx?&amp;No=')


These are mainly just nitpicks though. You're doing fine.