Vinyl
Vinyl flooring is the material most everyone considers when they imagine their kitchen floor, at first. Vinyl is available in a myriad of colors and styles to suit almost any decor. Vinyl comes in sheets/rolls 6' or 12' wide. Your first consideration when shopping for vinyl is whether your choice can be seamlessly installed in your kitchen (including coved baseboards, if used). Seams in vinyl flooring are always the first place to fail. Avoid them. Choose vinyl flooring with a minimum of embossing. Highly embossed floors trap and hold dirt making them difficult to properly clean. Exposure to strong sunlight can discolor vinyl flooring. Sharp objects can puncture and tear vinyl flooring. Moving heavy objects, such as your refrigerator, across vinyl flooring without protection can tear the material. Vinyl can not be repaired easily or very effectively. You may be surprised, when you compare, to find that vinyl costs about the same, installed, as longer lasting choices below.

Hardwood
Solid hardwood flooring has been used in homes for centuries with excellent, long-lasting results. Using hardwood in kitchens is a more recent phenomenon. We used to wax our hardwood floors, and wax and water don't mix (the wax coating turns white and milky).
Some years ago a Swedish firm began marketing a finish, Glitsa, in the U.S. that was very hard and durable, making wax obsolete. Kitchen designers and other specifiers discovered that smooth, reflective, warm hardwood makes a great kitchen floor and we have been encouraging our clients to use it ever since.
The use of Glitsa has diminished due to its toxic qualities, both for the homeowner and the worker doing the finishing. We are now using polyurethanes and the new water-based finishes. I recommend water-based finishes, even though they are not as long lasting as polyurethanes, because homeowners can touch up traffic areas themselves...That is, IF they have chosen a water-based finish.

Hardwood floors are easy to clean because they are smooth. Be sure that you choose material with no grooves for your kitchen to enjoy this benefit. Grooves catch and hold spills like sugar and are a nightmare to maintain.

Hardwood can be either finished on the job or prefinished. In our area, we usually use unfinished. With unfinished flooring the floors are sanded before finishing to get everything smoothed out. Then the finish is applied in layers.

If you choose the benefits of prefinished flooring material (longer wear, quick occupancy, lower installation cost), be sure to choose a manufacturer like Junkers (pronounced Yunkers), Junkers has a tongue and groove system that aligns every inch of every solid wood board that goes into your floor. The resulting installation is smooth and beautiful. Junkers also has a system that allows installation on concrete without extra height problems.

You are only limited by your imagination and budget when examining the various woods that are offered for flooring, everything from the ubiquitous red oak to bamboo to exotics. Stick with the colors that can be obtained by dyes, stains, fuming and finishes. Stay away from whitewashed or painted floors unless you have lots of discretionary money. They do not hold up.
Hardwood floors come in the colors of the original wood and darker colors created by stains. The smooth finish tends to be light-reflective in the light to medium tones. Very dark stains and wood show every speck of dust. The colors tend to yellow slightly over time, with exposure to sunlight and artificial light.
Solid hardwood floors are repairable and can be screened (only the finish is removed) or sanded and refinished to the extent of their thickness (typically 3/8" or 3/4"). They are easily cleaned with little effort due to their smooth surface. The only enemy is moisture, which can damage a floor if exposure is lengthy or constant. Minor splatters are really no concern with today's finishes.