Generally speaking you are not allowed to stay longer than what your visa states. What is allowed will depend on a few things: The “duration of stay”, the “from” and “until” fields and the number of entries.
Schengen visas do not necessarily allow a 90-day stay. Unlike the US, you will not be granted an authorization to stay for a particular period when showing up at the border checkpoint. Unlike the UK, you cannot receive a new “leave to enter” by crossing the border. Rather, the maximum period of stay is entirely defined by your visa.
Quite independently of the maximum duration of stay, you may not stay after the expiration of your visa either. Here again, Schengen visas work differently than US or Japanese visa (which need only be valid when entering the country).
The visa sticker will have a “duration of stay” field that determines the total number of days you may stay in the Schengen area on this visa. To the extent that you care about respecting the conditions of your visa, you cannot stay longer than that. It's only if the “duration of stay” says 90 or XXX (typically for multiple-entry visa with a long validity period) and the visa is still valid that the “90 days in any 180-day period” rule applies (that's probably what the Polish embassy meant).
To put it less formally, it's not 90 days from the date you enter or 90 days per entry, it's up to 90 days in total during the validity period of your visa (if you only have one visa valid for less than six months).
If you absolutely need to stay longer for serious reasons, you are supposed to approach the authorities to get an extension of your visa or, possibly, another type of visa but those are typically not granted merely for convenience.
If your visa does allow it, staying longer than what you submitted in your application is not per se a problem, as long as border guards do not suspect that the application was fraudulent.
If you do stay longer without authorization, you could be found out either when leaving the Schengen area (border guards are supposed to look for your entry stamp when you leave) or when applying for another visa. Not everybody will check so thoroughly but the discrepancy between the entry and exit stamps in your passport could still be detected later on. A new system is currently being rolled out and individual countries might have additional databases but there is no Schengen-wide computerized record of entries and exits to my knowledge.
The exact penalty for overstay depends on the country (it's not defined in the Schengen regulations) but it is usually a rather large fine (I have heard about several hundred euros, not just EUR 10-20 like parking tickets in some countries). There is also a mechanism to ban people from the Schengen area (although I would not expect a formal ban for a small overstay detected upon exit but I really don't know how frequent it really is). Obviously all of this is much more annoying if you plan to come back to Europe in the future.