What's the reason for going to the cost and effort of doing this?
In many places, placing a stream into a culvert can be cheaper in the long run. Streams (particularly fast flowing ones) erode the land and may require erosion protection added in the future.
An advantage is reduced land use: Land that does not have a stream running through it can be used for other purposes, although the culvert will need to, obviously, be assessed before plomping (technical term..) a multi-storey car park on top of it!
Is it a safety concern having creeks in residential areas?
Highly dependent on the area in question and the nature of the creek or stream. Naturally, a stream is a hazard to people of all ages, particularly kids though. But so is a culvert if the access to it is not cordoned off. As answered previously, an open grassy pitch is more favourable than a flowing stream.
Do creeks have some effect on the land which would affect nearby buildings?
Creeks have a tendency to meander in the long term (decades to centuries), and deeply scour the nearby banks in the short term (years). Scoured banks can become steep and rocky, and even collapse. If there are buildings located nearby, then this can cause structural damage.
Is it just for the convenience of being able to cross them without a bridge?
As an engineer with Highway experience you'd be amazed at how many culverts manage water flow run under many of our roads. 87
In Scotland, it's not unusual for there to be a 600mm diameter culvert every few hundred metres or so on many trunk roads and motorways helping ease water through them.
Most of the time, these are never seen or acknowledged as they can be down steep road verges. This is because these roads tend to be built very straight (much like railways), opposed to older roads that simply follow ancient paths and travelling routes.
A final note:
Culverts can be used to change the velocity of flowing water. For example if a stream has a narrow channel, the water will flow quickly causing it to quickly erode the bank. You can slow the water velocity in an area by passing it through a wide culvert. With a wider area of flow, the water will travel more slowly. This can cause advantages down stream. Similarly, the same effect can be caused upstream by forcing the water through a narrower passage. This will cause the water to back-up up stream reducing it's speed. 87