Ordinarily there is a three-month waiting period for Ontario Health Insurance Plan (OHIP) eligibility.
However, a member of the BE forum has discovered that it is possible, under certain circumstances, to get medical assistance before OHIP coverage begins. A member of his family received assistance with a pre-existing medical condition that was not covered by the family's temporary private insurance.
They were referred to a Community Health Centre (CHC). Normally CHCs provide family doctors to those who cannot find them (under OHIP coverage), but in exceptional cases (no clear rules defined) they also help new immigrants without OHIP.
Here is a list of Community Health Centres in Ontario.
It is worth noting that OHIP can be applied for once you have proof of address in Ontario. See the list of things needed to take to your local OHIP office to be able to apply at http://www.forms.ssb.gov.on.ca/mbs/ssb/forms/ssbforms.nsf/FormDetail?openform&ENV=WWE&NO=014-9998E-82 - as soon as you have bills in your name, you can apply (this seemed to be the thing that took the longest for us) - the application could be a month after you apply if you are able - they will still start your "3 month" wait time from the date of your arrival in the country, eg. if you arrive on 1 June, apply for OHIP on 15 July, your OHIP will be issued/valid on 1 September.
Also note that OHIP now covers people who are resident in Ontario and who have applied for Permanent Residence. In reality this only applies to In-Land applicants, as Service Ontario require proof from CIC of an Application of Permanent Residency addressed to the applicant. Out-Land Applicants will only receive such correspondence when successful as an applicant.
To find out how medical insurance and dental insurance in Canada generally work, please see the Wiki article called Medical Insurance-Canada.