Eating events or Sagre:
Pretty well every town and village throughout the Marche has some food or wine event during the summer months. Here are just a few of them :

June

Pianello (near Cagli) - Sagra della Lumaca (snails) - mid-June
Apiro (near Cingoli) - Sagra del formaggio pecorino (pecorino cheese)

July

Sefro (near Camerino) - Festa della Pizza - early July
Matelica - Sagra della Rana (frogs)
Ostra Vetere (near Corinaldo) - Festa della trota (trout) - earlyJuly
Montemarciano (near Senigallia) - Sagra del pesce (fish)
Corinaldo - polenta festival on third Sunday in July to commemorate the time when the town's people successfully resisted a siege thanks to copious supplies of the stuff.
Sefro (near Camerino) - Festa del Tortellino alla boscaiola (pasta) - late July
Castelplanio (near Jesi) - Sagra della crescia sul panaro (stuffed flat bread) - last Sunday of July
Ostra Vetere (near Corinaldo) - Sapori ed Aromi di Casa Nostra - late July - local food, music and a procession of old farm machines
August

Monte Vidon Combatte (near Fermo) - Sagra delle quaglie (quails) - 1st Sunday
Sassoferrato - Sagra del Cinghiale (wild boar)
Cingoli - Sagra di prosciutto e melone
San Severino Marche - Sagra della ceca (chick peas)
Staffolo (near Cingoli) - Festa del Verdicchio (verdicchio wine festival)
Fermo - Sagra delle vongole (shell fish)
Serra San Quirico (near Fabriano) - Sagra del coniglio in porchetta (roast rabbit with fennel)
Monteprandone (near San Benedetto del Tronto)- Sagra delle olive fritte (fried stuffed olives)
Pedaso - Sagra Nazionale delle cozze (mussels)
Massignano (near Ascoli Piceno) - Sagra delle frittelle (omelettes)
Vererotta (near Ascoli Piceno) - Sagra della vitella allo spiedo (spit-roast veal)
Loro Piceno - Sagra del Vin Cotto (a sweet "cooked" wine)
September

Apiro (near Cingoli) - Sagra della polenta
Montecassiano - Sagra del pesce (fish)
Cupramontana - grape festival in the heart of Verdicchio wine country in September.
Piandimileto (near Urbino) - Mushroom fair
Lapedona (near Fermo) - Sagra del Vino Cotto (the Marche version of Vin Santo)
Fermo - Sagra della Polenta
Arcevia - Sagra dell'uva (grape festival)

October

Acqualagna (near Cagli) - Fiera nazionale del tartufo (truffle fair) - last weekend in October and first two weekends in November in the town that calls itself the "truffle capital".
Acquasanta Terme (near Ascoli Piceno) - Festa d'autunno (autumn produce)
Montemonaco (near Ascoli Piceno) - Sagra della Castagna (chestnut)
Castelsantengelo sul Nera (near Visso) - Sagra del Marrone Castellano (chestnut)
Sant'Agata Feltria - White Truffle fair
Sant'Angelo in Vado (near Urbino) - Mostra del tartufo bianco (white truffle)

November

Talamello (near San Leo) - Formaggio di Fossa cheese fair
Acqualagna (near Cagli) - truffle fair - last weekend in October and first three weekends in November in the village that calls itself the "truffle capital".
Fun & Games:

Ascoli Piceno La Quintana - jousting in Ascoli's main square on the first Sunday of August. The most authentic "medieval" goings-on in the Marche.
Urbino Festa del Duca - a jamboree in honour of Duke Federico on the third Sunday in August.
Cagli Palio dell'Oca - medieval games to win a golden goose in mid-August.
Mondavio Wild Boar Hunt - a medieval chase in the square - very jolly. mid-August.
Fermignano Palio della Rana - yes, a race with frogs in wheelbarrows - the joint is really jumpin' on the first Sunday after Easter.