Perennial Leeks

Perennial leeks taste like every day leeks, but they have bulbs and give side shoots, forming perennial clumps which spread and are very resistent to drought or frost. This is a must have for permaculture and perennial vegetables enthusiasts.

http://www.cornucopiaseeds.com.au/products/Perennial-Leek.html

Walking Onions and other relatives

Another "must have" for Permaculture enthusiasts are Walking Onions, also known as Egyptian Onions (Allium proliferum). These are perfectly normal onions which give flowering tips which produce bulbs which fall and give way to new onion plants, hence the reason for its name for the plant that seems to walk through the garden!

The bulbs are however small.
Perhaps even more interesting (although I don't own these yet) are Multiplier Onions (Allium cepa aggregatum), which produce bigger bulbs in clumpings. Both species are edible and taste like onions.

Welsh onions (Allium fistulosum), Ramsons (Allium ursinum) and Chives (Allium schoenoprasum) are other perennial options. Chives taste wonderful in omelletes. Ramsons can grow native in shade in European forests and give many white flowers in spring; the plants look very similar to other poisonous species like the Lily-of-the-valley, but they have a strong smell of garlic.

Danger of wrong identification of wild carrot family herbs

Whenever you go finding and identifying wild edible herbs, you must be very careful in the proper identification of species from the carrot (Apiaceae) family.

Never collect and eat plants from this family from the wild, since some are very similar between each other and also very poisonous. They can be frightening similar to parsley, chervil, carrots or parsnips. Some even smell carrot-like and have sweet flavours! Nevertheless, small ammounts can cause death by muscle paralysis.
Some examples are:

• Fool's Parsley, Aethusa cynapium
• Hemlock, Conium maculatum
• Water dropwort, Oenanthe crocata
• Water hemlock, Cicuta spp.
  

http://en.wikipedia.org/wiki/List_of_poisonous_plants