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 in Europe 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. However it is thought that the slight incompatibility with quince is also important in the size control and precocity these rootstocks induce.
In North America, the most popular rootstock series is based on a cross between two pear varieties, Old Home and Farmingdale. Different forms have different vigours, but all have good cold-hardiness and fireblight resistance, which are important characteristics in the US climate. Being Pyrus in origin, these "OHxF" rootstocks do not have the latent incompatibility between pear and quince which is inherent in the Quince-derived rootstocks.
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.
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 is the most widely-planted semi-vigorous rootstock for pears in the UK, and is also quite popular in the USA, even though it lacks the cold hardiness and blight resistance that is really needed in some of the colder zones of the USA. Pears grafted on to the Quince A rootstock produce trees with a height after 5-10 years of 3m-4m / 10ft-14ft or so - 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).
In this "33" form produces a semi-vigorous tree of about the same size as Quince A, and roughly half the height of a seedling pear tree. It is popular in the Pacific North West of the USA but less so in the eastern pear-growing areas.
Produces a tree somewhat larger than Quince A, and perhaps 50% - 70% of the size of a seedling pear tree, so perhaps 4.5m - 5m or around 16ft-18ft. PyroDwarf is a good alternative to seedling rootstocks, as it produces large attractive trees which nevertheless start bearing quite young, usually after 3-4 years. Being of Pyrus origin, there are no graft incompatibility issues with this rootstock. PyroDwarf is able to tolerate chalk / alkaline soils better than quince-derived rootstocks. PyroDwarf was developed from a cross between Old Home and Louise Bonne pear varieties, but has only inherited some of the former's fireblight resistance.
In this "87" form produces a semi-vigorous tree of about the same size as PyroDwarf, and roughly two-thirds the height of a seedling pear tree. It has good winter-hardiness and blight resistance, and is widely planted.
In this "97" form produces a full-size tree of around 20ft.
Pyrus communis (Kirchensaller)
The Pyrus "rootstock" is used for producing large specimen pear trees. This is basically a pear seedling and hence is the equivalent of growing a pear tree on its own roots. It is compatible with all pear varieties and eventually produces a very large tree - well over 6m / 20ft, and usually very long-lived. It can be grown on most soils and is tolerant of chalk.