There are only six Trappist monasteries brewing beer, or at least only six that sell it. The products are all top-fermented ales, and are only sold bottled, with the exception of Chimay Triple which is also now available on draught:
Westvleteren is almost impossible to obtain except by visiting the abbey yourself, but the others are fairly widely distributed in Belgium (you will be able to find two or three in almost any bar and most in any supermarket) and exported (particularly Chimay); they all now carry a hexagonal "Authentic Trappist product" label. The three Walloon monasteries - Orval, Chimay and Rochefort - also produce and market their own cheese and bread, also carrying the same mark.
A large number of other Belgian beers are sold as "Abbey beer" of one place or another; this is just marketing and the links with monasteries range from purely commercial to highly fanciful; for example, the beers sold as being from the Maredsous abbey near Dinant are in fact made by the Moortgat brewery in Antwerp (mainly noted as brewers of the far from holy Duvel), while the Leffe range is named for a defunct abbey also near Dinant and is a purely industrial product made at various Interbrew plants across Belgium. Many of the abbey beers are, nonetheless, perfectly drinkable.
A seventh one to add to the list (thanks to bbibber - the abbey at Achel, on the Belgian/Dutch border, has just restarted brewing after an 80 year hiatus since their equipment was commandeered by the Germans during the First World War occupation of Belgium).
Down to 6 again. Chelman informs me that the monks at Koningshoeven are no longer producing La Trappe in house and have renounced any formal connection with the brewers, so it has been downgraded to an abbey beer and does not bear the "Authentic Trappist Product" label any longer, although it is still being sold as "trappistenbier", a tag which is used by several beers in the Netherlands which apparently merely relates to the brewing style and not the provenance.
It is worth noting that the monastery at Achel is in fact a daughter house of Koningshoeven Abbey, so there may be some connection with the renewal of brewing there - anyone up on Cistercian internal politics feel free to /msg me...
La Trappe is now (2007) officially a Trappist product once again - thanks cpschnei.
Thanks to mkb for spotting the existence of draft Chimay