Rootstocks for Pear trees
The choice of rootstocks for pear trees is more limited than it is for apples reflecting the fact that pears are not as commercially important as apples. Whereas rootstocks for apples and plums come from closely related Malus and Prunus species respectively, the situation with pear rootstocks is more unusual. The most widely-used rootstocks for pears come not from another pear species, but from a different species altogether - Quince (Cydonia oblonga). However, as is obvious from the shape of the fruit, there is still a close relation between quinces and pears which means that pear scions can be successfully grafted on to quince rootstocks. Quinces tend to be smaller trees than pears, and quince rootstocks also encourage precocity, in other words the resulting tree bears fruit at an earlier stage in its life than a pear tree on its own roots, usually within 3-5 years.
One side-effect of the more distant relationship between pear species and quince rootstocks is that not every pear variety is compatible. Where this happens an "inter-stock" or "interstem" has to be used, and the resulting tree consists of three parts - the quince rootstock, the inter-stock (which is often a pear variety such as Doyenne du Comice which has good compatibility with quince) and then the fruiting variety.
Although pears cannot be grafted on to apple rootstocks, some pear varieties can be grafted on to an apple rootstock via an interstem of the apple variety known as Winter Banana which seems to have some compatibility with pears. Perhaps even more surprisingly, it is possible to graft pear scions directly on to hawthorn roots (Crataegus), reflecting the fact that pears and hawthorns are both members of the rose family (Rosaceae) as are apples, plums, and cherries. However hawthorn rootstocks are not really suitable for pear trees used in garden situations.
Quince C
Pears grafted on to the Quince C rootstock produce the smallest pear trees. The height after 5-10 years will be about 2.5m to 3m or so.
Quince A
Pears grafted on to the Quince A rootstock produce trees with a height after 5-10 years of 3m or more - in other words larger than the same variety on Quince C but not dramatically so. It can be considered roughly equivalent of the apple MM106 rootstock - so if you want to plant a pear and an apple tree and want them to have similar proportions then choose Quince A and MM106 rootstocks respectively. (However be aware that pear trees tend to have a more vertical habit than apple trees).
Pyrus
The Pyrus "rootstock" is sometimes used for producing large specimen pear trees - it is the equivalent of growing a pear tree on its own roots, and eventually produces a very large tree - more than 6m, and usually very long-lived.