The family tree of angiosperms underwent a revolution in the 2000s. A group of experts called the Angiosperm Phylogeny Group (APG) revised all the orders and families in the light of newly-available DNA evidence. In many cases they made major changes to the circumscriptions (what was covered by what), moved things around, cut things up, and made surprising connections. They also departed from Linnaean taxonomy by creating some major clades that didn't have specific ranks, but indicated important groupings. These they wrote in bold lower-case. The APG classification was followed several years later by a revision APG II, and we are now at APG III.
First, the traditional primary distinction between monocotyledons and dicotyledons proved to be only half true. There is still a true clade, which they call monocots, covering grass and onions and daffodils and the like. Most of the old dicotyledons are assigned to a parallel group called eudicots. The rest are mostly in a third parallel group, magnoliids. Parallel here means we don't yet know how to resolve the trichotomy: one of the three groups branched first, but it is difficult to tell which. However, outside these main groups are three smaller orders, Austrobaileyales, Nympheales (the water lilies), and Amborellales, the last an entire order created for a single New Caledonian plant. This is seemingly the cousin of all the rest: the ancestral angiosperm divided into the ancestor of Amborella and the ancestor of all other angiosperms.
Inside monocots there is a major group called commelinids. Inside eudicots there is a major group core eudicots, which includes two groups asterids and rosids. At each level there may also be some orders (or families removed from former orders) that are part of the level but not part of any major group below. These are called basal. For example, basal eudicots include orders Ranunculales and Proteales and (in APG II) family Buxaceae not in any order; eudicots includes those as well as the larger clade core eudicots. (In APG III it was neatened up by giving Buxaceae its own order Buxales.) The final layer of these bold new clades is that each of asterids and rosids has two major subclades, and these are called euasterids I, euasterids II, eurosids I, and eurosids II.
Plant orders always end in -ales, and they contain families ending in -aceae. A family is named after one of its genera, and an order is named after one of its families. So the family containing grasses is named Poaceae after a particular grass genus Poa, and is accordingly referred to as the grass family. (This is just a convention: the 'rose' family contains blackberries and apples and almonds, and many others. They're all Rosaceae and all in the rose family but they're not considered roses, not even by theoretical biologists.) The order containing the grass, rush, and sedge families is called Poales. The order containing the rose, fig, and cannabis families is called Rosales. Eight traditional and very well-known family names not ending in -aceae have been preserved as alternatives; so Poaceae is also called Gramineae.
So the lower-case plural names of the new clades was a bold step. I am particularly impressed by the daring of those Roman numerals in the likes of euasterids I. (The bold face was how they were first presented: I don't know whether workers in the field really bother with it. The names are perfectly good and distinctive without it, and to save wear and tear on my HTML I'll drop it hereafter.) My only quibble is that the name order Asterales is in euasterids II, unexpectedly. Since these name were first given, slightly more conventional alternatives have been proposed, naming them after one of the groups inside them: so euasterids I, euasterids II, eurosids I, and eurosids II are also known respectively as lamiids, campanulids, fabids, and malvids.
Orders and families: and examples
On a good day I can place the 40-odd orders I've memorized, and several times that many families in them. There are more orders, and many more families, and serious sites elsewhere on the web list them all. I just want to give an overall view here, so I'm going to name only the orders and families that contain plants I've heard of. These orders cover the great bulk of the angiosperm world. Even these 40 can't be fitted neatly in a tree on one sheet of paper, and the list below is inevitably going to be messy too. The common names I mention below, such as magnolias, laurels, and peppers, are just typical members, not definitions, and sometimes they're products (such as camphor). If I don't mention a family, you can take it from the order: bay laurels are in order Laurales, so you can interpose the family Lauraceae by the standard naming rule. Note there are some common names that have multiple hugely different meanings (e.g. chestnut, hemlock, laurel, lime, loosestrife, pepper, plantain, sycamore, yam); I've added clarifications for these, if it's not obvious from the taxonomic location.
Nymphaeales: water lilies
The magnoliids include:
Laurales: bay laurels (but not spotted or cherry laurels), avocado, cinnamon, camphor, sassafras
Piperales: peppers (black and white, not red and green)
The monocots include:
Arecales: Arecaceae or Palmae: palms (incl. date, coconut)
- Poaceae or Gramineae: huge family including grasses and reeds, bamboo, sugar cane, and grain crops such as wheat, oats, maize, rice, barley, rye
- Cyperaceae: sedge, water chestnut, papyrus
- Juncaceae: rushes
- Typhaceae: bulrushes/reedmace
- Bromeliaceae: bromeliads, pineapple, Spanish moss
Alismatales: Araceae: arum, monstera, philodendron
Dioscoreales: yam (the ones that are white inside, not orange sweet potatoes)
- Asparagaceae: asparagus, bluebell, hyacinth, agave, aloe, aspidistra, lily-of-the-valley, red-hot poker (Kniphofia)
- Alliaceae: onion, garlic, leek, daffodil, snowdrop, agapanthus
- Iridaceae: iris, crocus, freesia, gladiolus
- Orchidaceae: orchids, vanilla
The eudicots include:
Caryophyllales a large and surprising group
- Ericales a large and diverse group
- Ericaceae: heather, azalea, rhododendron, cranberry, blueberry, kalmia
- Primulaceae: primrose, cowslip, oxlip, polyanthus, cyclamen, scarlet pimpernel, yellow loosestrife
- Actinidaceae: kiwi fruit
- Balsamaceae: balsam, busy lizzie (Impatiens)
- Ebenaceae: ebony, persimmon
- Lecythidaceae: Brazil nut
- Polemonaceae: phlox
- Sapotaceae: chicle (for chewing gum), gutta-percha
- Theaceae: tea, camellia
Santalales: sandalwood, mistletoe
- Caryophyllaceae: carnation, campion, sweet william, stitchwort, baby's breath (Gypsophila)
- Amaranthaceae: beet, spinach, quinoa, celosia
- Polygonaceae: buckwheat, dock, rhubarb, sorrel
- Aizoaceae: mesembryanthemum
- Cactaceae: cactus
- Droseraceae: sundew, Venus fly trap
- Nepenthaceae: pitcher plant
- Nyctaginaceae: bougainvillea
- Plumbaginaceae: plumbago, thrift (Armeria)
- Simmondsiaceae: jojoba
- Tamaricaceae: tamarisk
Now for some of the largest groups, which won't reasonably fit in the upper-level tables above.
euasterids I (lamiids):
- Lamiaceae or Labiatae: basil, lavender, mint, oregano, rosemary, sage (Salvia), thyme, dead-nettle (Lamia), bugle, selfheal
- Oleaceae: olive, ash, jasmine, lilac, forsythia, privet
- Plantaginaceae: plantain, foxglove, snapdragon, speedwell, hebe, penstemon, toadflax
- Acanthaceae: bear's breach/brank-ursine (Acanthus)
- Bignoniaceae: catalpa
- Calceolariaceae: calceolaria
- Gesneriaceae: African violet
- Orobanchaceae: broomrape, yellow rattle
- Pedaliaceae: sesame
- Scrophulariaceae: buddleia
- Verbenaceae: vervain (Verbena), teak, lantana
- Solanaceae a mix of delicious foods and deadly poisons: potato, tomato, red and green pepper (Capsicum), aubergine/eggplant, goji, physalis, petunia, tobacco, deadly nightshade, mandrake, henbane, bittersweet
- Convolvulaceae: bindweed, morning glory, sweet potato
Garryales: spotted laurel (Aucuba)
Boraginaceae (basal family not in any order): borage, forget-me-not, comfrey, alkanet, pride of Madeira, cherry pie (heliotrope)
- Gentianaceae: gentian
- Rubiaceae a very large group, including: coffee, gardenia, bedstraw, goosegrass/cleavers, woodruff, quinine (Cinchona)
- Apocynaceae: periwinkle, frangipani, oleander
euasterids II (campanulids):
- Asteraceae or Compositae a gigantic family: daisy, thistle, lettuce, dandelion, sunflower, aster, artichoke (both kinds), burdock, camomile, chrysanthemum, cineraria, cornflower, dahlia, gazania, goldenrod, groundsel, marigold, ragwort, safflower, tansy, tarragon, wormwood, yarrow, zinnia
- Campanulaceae: bellflower, harebell, lobelia
- Apiaceae or Umbelliferae: carrot, parsnip, celery, parsley, dill, fennel, anise, angelica, caraway, cow-parsley, hemlock
- Araliaceae: ivy, ginseng, fatsia
eurosids I (fabids):
Fabales: family Fabaceae or Leguminosae: pea, bean, lentil, soya, chickpea, peanut; broom, gorse; mimosa, wattle (Acacia), sensitive plant; alfalfa/lucerne, clover, kowhai, laburnum, liquorice, lupin, rosewood, tamarind, wisteria
Celastrales: qat, euonymus (This and the next two orders, Oxalidales and Malpighiales, form a clear clade together, COM.)
Oxalidales: wood sorrel (Oxalis)
Malpighiales (a baffling array of families with little overt similarity to show for the genetic relationship)
- Rosaceae: rose; blackberry, raspberry, strawberry; apple, apricot, cherry, peach, pear, plum; almond, cherry laurel, cotoneaster, hawthorn, kerria, quince, rowan, spiraea, wood avens
- Cannabaceae: hemp (Cannabis), hops
- Moraceae: fig, mulberry, breadfruit, banyan
- Rhamnaceae: buckthorn, ceanothus
- Ulmaceae: elm
- Urticaceae: (stinging) nettle
eurosids II (malvids):
- Malvaceae an astonishing diversity now brought into the one family: mallow, hibiscus, hollyhock; lime/linden; abutilon, balsa, baobab, cacao (chocolate), cotton, durian, kapok, kola, okra
- Cistaceae: rock rose (Cistus)
- Thymelaeaceae: daphne
- Brassicaceae or Cruciferae: Brassica (cabbage, cauliflower, broccoli, Brussels sprout), mustard, cress, radish, horseradish, swede, turnip, wasabi; aubretia, candytuft, honesty, rapeseed/canola, thale cress (Arabidopsis thaliana), Virginian stock, wallflower, woad
- Capparaceae: caper
- Caricaceae: pawpaw/papaya
- Tropaeolaceae: nasturtium
Myrtales This and Geraniales form a clear clade, the sister of the rest of eurosids II.
- Sapindaceae: maple, sycamore, horse chestnut, lychee, guarana
- Rutaceae: citrus (orange, lemon, grapefruit, lime, kumquat), rue, choisya, boronia, correa
- Anacardiaceae: cashew, pistachio, mango, poison ivy
- Burseraceae: frankincense, myrrh
- Meliaceae: mahogany
Geraniales: cranesbill (Geranium) and the garden geranium (Pelargonium)
- Myrtaceae: myrtle, gum (Eucalyptus), bottlebrush (Callistemon), tea-tree, clove, guava
- Onagraceae: evening primrose, fuchsia, willowherb, enchanter's nightshade
- Lythraceae: purple loosestrife, pomegranate
Inevitably this will have proof-reading mistakes in some of the taxon names, and be missing some of your favourite plants. Possibly the best detailed website on the APG III classification (with copious explanation) is the Angiosperm Phylogeny Website. A simple one-page table of all the orders and families is at The Seed Site. The web's other free encyclopaedia is also using APG III now, and compares current taxa to more traditional ones, which is very useful.
2014-05-22 Added order Pandanales; families Altingiaceae, Dipsacaceae, Haemodoraceae, Hamamelidaceae, Pedaliaceae, Smilacaceae, and Tamaricaceae; and 20-odd common names, mostly ones that are familiar names though I don't actually know what they are, such as catalpa, goldenrod, kowhai, liquidambar, philodendron, sassafras, tamarind, and witch hazel.
2014-05-29 Tch, ivy is not holly!
2014-06-25 Add mock orange (Philadelphus)
2015-06-15 Palmae is family Arecaceae, not order Arecales. Add Orobanchaceae.
2015-06-22 Peonies are in Paeoniaceae, not Paeonaceae; but dogwood is Cornaceae in Cornales, not Corneaceae in Corneales. Add rye.