The most popular hike on Table Mountain
I would guess that the most popular hike on Table Mountain is Platteklip Gorge. Although this is an incredibly beautiful and scenic hike, I don’t believe its popularity is due to its scenic splendour as it is no greater in this regard than several other routes up Table mountain.
The popularity of Platteklip Gorge is due to it being close to the city and the top being 5 minutes from the cable car. Thus people with limited time in Cape Town can hike up Table Mountain in 2 to 2.5 hours, enjoy all the classic views from the top and then take the cable car down. The entire trip having taken less than 3 hours. Other well known routes, for example Skeleton gorge or Kasteelspoort are still a 2 hour walk from the cable car once you get to the top of them. An added complication would also be getting back to your car. The bottom of Platteklip Gorge is only 2km from the lower cable way station whilst Skeleton Gorge and Kasteelspoort are both a good 30 minute taxi drive away.
Of course the popularity of Platteklip Gorge does mean that you do not quite escape the crowds as you on the other routes. On a nice Saturday morning you may encounter 20 or 30 people on Platteklip whilst on one of the other routes you will probably only see 4 or 5 other people. (bear in mind that 600 people an hour will be going up by the cable car, so to describe any hike on Table Mountain as crowded is a very relative concept.)