A regular mower will not give the best results, esp. with deep layers of leaves. This is because the mower will expel the leaves from underneath the deck before they are fully chopped into small shreds. Even with repeated passes over the leaves, the result may not be acceptable.
What is needed is either a mulching kit accessory (for the existing mower) which closes off the output port of the mower deck, or an upgrade to a true mulching mower.
Many companies make mulching mowers for both homeowner market and for the professional landscaper market. Under the Homeowner tab (near the bottom of the page), there are links to various product pages. One of these links is to an Amazon.com page of walk-behind mulching mowers (consumer grade, not professional grade). Such mowers can range between $150 to $350 depending upon brand, size of blade and so forth. (Professional landscaper mowers are typically more expensive.)
Mulching mowers can also be found at Home Depot, Sears, and other similar stores.
We recommend that if selecting a gas powered mower, a mower with at least 7 ft-lbs of torque be chosen. If selecting an electric mower, a 12 or 14 amp motor is good.
For further information, see this FAQ: What equipment do I need to mulch my leaves?