Since the widespread use of GPS cable routes are very accurately known and cable and pipeline crossing points have to be determined and negotiated when a new cable is laid.
Especially on continental shelves where (down to about 1000m water depth - sometimes deeper) they are armoured cable and typically laid in a ploughed trench 1-2m deep on the seabed. The major damage hazard at these depths is by trawl boards as fishermen trawl for weirder and weirder fish at greater depths.
You really don't want someone ploughing through your cable (or pipeline) when laying a new one. because of this danger, cable crossings are very carefully planned and engineered, usually achieved by stopping the plough 1-2 km back from the the crossing site, surface laying the new cable over the cable to be crossed, then retro burying it using powerful water jets on a ROV. Sometimes gravel is dumped over the crossing site to give additional protection.
In shallower waters as another commenter said it may be dragging anchors. That may required deeper burial and double armoured cable The worst possible place is where supertankers or large container ships anchor nera cable landing points- especially Singapore and HK harbours Singapore has its own specialised burial barge permanently stationed there which can bury up to 20m deep!
Less common hazards are cables wearing through by "thrumming" over exposed rock surfaces in seabed level currents (rare and try to avoid these hazards when planning cable routes) and cable breaks by slumping in undersea landslips sometimes triggered by earthquake activity ( gain avoid laying across steep slopes )
Early deep sea cables in the Atlantic were sometimes attacked by deep sea sharks (Goblin Shark) with an electric sense - the field caused by the power cable that feeds the repeaters looked to the shark like a big meal. All cables since about 1988 include an aluminium tape "screen" layer to shield this field