Latency differences between our senses
Given your questions taken together and your comment It would be interesting to know how much delay the brain can handle in understanding causality and associating events I think you are interested in intersensory asynchrony. A well-known example where two stimulus modalities are perceived as separate while they are in fact coming from the same event is a thunder heard after lightning. This is caused by the fact that sound travels at a speed much slower than light, and hence a thunder can lag lightning by seconds.

source: NASA
In many instances, however, one event generating perceptions across stimulus modalities are actually perceived as synchronous while they are in fact offset in time due to differences in physical characteristics of the stimuli. Taking the storm as an example - when it is far away, the thunder is perceived as separate because the thunder lags by seconds. But when the thunderstorm is close enough, the auditory crack and visual lightning are actually perceived as synchronous, while in fact they are still offset because of the sound travelling so much slower than light.
So the question becomes, as you rightfully ask, what are the margins in which stimuli across modalities can be asynchronous while perceived as one event? In other words, what is the window of integration?
A review by Vroomen and Keetels (2010) describes various psychophysical studies that have examined what the minimal asynchrony is between two stimuli of different modality that lead to a synchronized percept. The following values are for simple stimuli, such as tactile taps, auditory beeps and visual flashes.

Auditory and tactile stimuli: 80 ms
Auditory beeps and visual flashes: 25 - 50 ms
Visual and tactile stimili: 35 - 65 ms

Note that these lag differences are relatively large, given the speed of peripheral neural transduction (see the other answer of Nandor Poka below). Moreover, the window of integration between more complex stimuli can be much greater. For example, the window for speech and visual information can be as large as 203 ms.  Such large windows of integration point toward higher processes playing a role in the brain.
Note that only temporal lags below 20 msec are expected to go unnoticed because of hard-wired limitations on the resolution power of the individual senses,
Hence, Vroomen and Keetels (2010) argue there must be higher processes at work in the brain that actively synchronize percepts that are offset in time, but seem to belong to one and the same event. One such mechanism is referred to as temporal ventriloquism, which means that one perceptual modality is actively shifted in time to match it with another. This effect is most pronounced in visual stimuli, in that a visual percept is actively adjusted in time to match a sound or tactile stimulus. Likely visual percepts are shifted preferably by the brain, because the visual system is the slowest of all the senses.
Reference
- Vroomen &amp; Keetels, Att Percept Psychophys 2010; 72(4): 871-84