If laid correctly there is generally no problem with mulches. However, if they are in direct contact with the stems of trees or specimen shrubs they can cause the stem to soften, making it vulnerable to diseases.
To save water and suppress weeds, the type of organic material you choose is less important than putting on a thick enough layer. Thicker layers will block sunlight from weeds, insulate the soil better and reduce the amount of water evaporating.
Depending on the quality of the material there is a possibility of introducing weeds, pests and diseases to the garden and, with woodchips there is a slight risk of introducing honey fungus.
Once you have added a mulch to the soil you may need to apply extra water to reach the roots of the plants beneath, but mulch will also help rain to soak into the soil, and less water will evaporate, so you should find you need to water less frequently.
Using freshly chipped material such as woody prunings or grass clippings can encourage the microorganisms in the soil to grow but they may use up reserves of nitrogen, leaving less available for plant growth. If you have freshly chipped material, keep it stored for a few weeks before using.
There is no need to remove mulches to apply fertilisers. Fertilisers are spread over mulches in late winter and are washed down to plant roots by rain.
Avoid damaging roots of plants by hoeing weeds growing in mulches around permanent plants. Remove weeds by hand and add a further layer of fresh mulch.
Organic mulches can be easier to maintain as they can be replaced by adding another layer when it has completely rotted away. Gravel can sometimes mix with the underlying soil if not applied thickly, encouraging surface weeds.
It is not uncommon for the white fungal mycelium of harmless saprophytic fungi to be found in soil that has been covered or enriched with an organic mulch. This is nothing to worry about and there is no need to dig out the mulch or white fungal growth.