Depends on the time period. I can't find the sources I learnt all this from, so I'll go with a lot of illustrations rather than books, but I'll only use art that was pretty close to what I know was common.

If we count Carolingian 'milites' as knights, then their shields were round (or oval), concave and had a highly raised boss (pretty much a spike). Here's some pics from the ninth century. It has been suggested that this is just an artistic convention borrowed from Byzantine art, and that the real shields may not have looked much like this, but here's an article that disagrees (third section). From about 1000 the most common design was the 'kite' shield that is shown on the Bayeux tapestry (two with dragons or dogs and a picture showing the backs, with the straps and handles) Kite shields were mostly convex too. After a while the style changed from a curved to a flat top (the front guy in the last picture, and this one from 1200) From there they developed into a smaller more triangular shape, known as 'heater shields' more like these guys' ones from the 1230s (entirely unrelated, here's some hedgehogs collecting grapes on their spines from the same book). The shield of Edward the 'black prince' (died 1376) is also of this type (there's a better photo as well in black and white)

This was the most popular style for mounted knights up until the late 14th/early 15th centuries, when armour became so good that most knights stopped using shields at all. At the same time a design with a notch cut out for a lance was developed (here it is on an oval shield) though these became pretty much only for tournaments after a while.

There were a number of other medieval shield designs, but most of them were used by poorer soldiers, or only on foot, so fall outside the scope of the question.