With SLR cameras, the viewfinder (the thing you look through) shows you (almost) exactly what the film/sensor will see. As has already been said, a mirror goes between the sensor and lens, and diverts the light to the viewfinder. When you take the picture the mirror moves out of the way. This allows the visible image in the viewfinder to match the captured image without parallax, be very similar in magnification and identical in focus/depth of field.
Compact cameras don't have the mirror mechanism - so have a seperate viewfinder, which gives an approximation to what the main lens will see. It's inaccurate due to parallax error, may be inaccurately matched for magnification/zoom, and cannot show the focus position or depth of field.
In order to deal with the focus problem - some manufacturers invented rangefinder cameras. These added a rangefinder mechanism to the viewfinder. This makes it possible to see the distance to the subject, so that the main lens can be precisely focused on the object of interest.
Now that autofocus is practical for compact cameras, rangefinders are unnecessary.
One advantage of digital sensors is that it is possible to get a live preview - this means digital compact cameras can produce a precise preview (without parallax and showing focus) of the scene. The problem, is that the LCD image often isn't sharp enough to focus with (this is the case with my compact canon - although it has a manual focus function, it is unusable because the screen resolution isn't anywhere near good enough) - and some sensors need significant time to switch from live preview mode to full capture mode.
I'm not aware of any cameras that reflect the image between the lens and the film. Although there may be some, every camera I've seen places the film/sensor immediately behind the lens. This isn't the case with video cameras, where high end cameras use a series of coloured mirrors to reflect red, green and blue light onto 3 seperate CCD sensors. This allows higher resolution and less noise. A standard full colour sensor throws away 2/3 of the light it receives in its filters. 3CCD systems use 100% of the light, diverting each of the different colours to a dedicated unfiltered sensor. This three sensor/mirror arrangement is expensive and bulky, so is reserved for pro and pro-sumer video cameras.
With conventional film cameras - the image quality is really dependent upon the quality of the lens and the quality/sensitivity of the film. A cheap moulded glass fixed-focus lens isn't going to give the same quality as a precision aspheric ground, multi-coated, lens made from special refractive glasses. Similarly, consumer grade film isn't going to give the same resolution, colour and contrast as pro film - but it's cheaper, and is designed to age well, whereas pro film is designed to be used as fresh as possible, kept refrigerated, developed immediately after shooting, etc. There are compact film cameras of outstanding quality (e.g. Leica) - because they use precision engineered lenses - however, they still suffer from the same limitations as other compact cameras - mainly that you don't see exactly what gets recorded on the film.
In terms of digital cameras - the SLRs are bigger, designed for a higher price point, and so can use bigger, more expensive sensors. With image sensors, size is king - Bigger gives you less noise and/or better resolution - which are both the major limiting factors in digital image quality. Base model dSLRs use APS size sensors (23 x 15 mm). Pro-level SLRs use larger sensors (up to 36x24, or even larger for studio cameras e.g. 49x37 mm). The other major selling point of digital SLRs is their flexibility - interchangeable lenses mean that you can choose the lens best suited to your subject - e.g. a very high magnification zoom lens for sport or wildlife, or a very wide angle lens for architecture or landscapes - or your budget e.g. a $250 general purpose lens for a beginner, or a $2000 high-magnification 'telephoto' lens for a pro who must have the best, sharpest picture of a charging wildebeest. There are other minor differences between the dSLRs and non-SLRs - again, the higher price allows more functions: better autofocus sensors, better shutter mechanisms with better precision or range of speeds, etc.