Organic gardening used to be unconventional; it's changing to be the usual now, I suspect.

I do unconventional gardening by using a lot of animal manure from the farm (rather than buying a few bags of it at Home Depot!!).

Composting used to be unconventional but now everybody is buying those little turners.

Old radical ways like growing potatoes under hay or straw or newspapers is unconventional; I use dirt, so that's conventional.

I use chemicals and love 'em all -- that's probably unconventional these days, to use herbicides, inorganic fertilizers, and insecticides/fungicides. Works better, though. [:-)

Really, it's not clear what IS conventional versus rare these days.

Much of what was unconventional even a few years ago is now conventional. Depends also on whether we are taking 'back-yard' or commercial gardens. Some are difficult to pigeon-hole such as heirloom plant varieties because they were once conventional, became unconventional when newer varieties were developed, and now may be becoming somewhat conventional again for those who appreciate their qualities.

Conventional:

Fertilization/weed eradication/insect control with synthetic chemicals
Vegetables in rows
Tree fruit farming with large fruit trees

Unconventional:

Use of humanure and urine, and the various organic composting and soil amending methods. At one time this was conventional, is now unconventional, but becoming more conventional altho I'm sure humanure and urine are still mostly unacceptable.
Weed control with mulches and organic or physical methods.
Insect control using good gardening practices, organic sprays, and beneficial insects
Square foot gardening
Trees bred for small size with good size fruit - becoming conventional in many/most commercial tree fruit farms.
Heirloom plants

I try to garden as organically as possible.

Here in the USA, USDA certified Organic gardening/farming is defined by law, if you intend to label your produce and sell it as "USDA Certified Organic." If you use the word "organic" on a label, then you must conform to the written, defined, legal methods and allowed input materials. For home gardeners with no intent to sell, organic generally means growing produce without synthetic pesticides, and without synthetic fertilizers.
Conventional agriculture is a phrase used to describe farming with modern methods, including the use of synthetic fertilizers and synthetic pesticides. However, methods and inputs continually shift over time. If you want to be clear about what you mean, then you would have to give a geographic location, and a year. So I might say "conventional dairy farming, Dane County, Wisconsin, 2010."
Personally, I garden without synthetic pesticides, but I do use synthetic fertilizer, in small amounts, along with inputs that organic gardeners make use of.