For those who know they need to get out away from the shore but are short of funds for a motor, trailer, and boat, for those who have despaired of their fishing boats for the time spent getting to the water and burning expensive quantities of fuel once there, and especially for those looking for a greener fishing alternative, a specially engineered kayak is a great solution.
Kayak fishing is getting more and more popular--there are magazines and web sites devoted to it--and with very good reasons. You're no longer shore-bound, and you have a small enough craft to launch from nearly anywhere. You buy and burn no gas while on the water, and in fact you benefit from the exercise of paddling. You might spend less time getting to fishing spots: I live a five minute walk to a beach, but a twenty minute drive to the marina. I can be on the water, including the walk, faster than I could get to the marina and launch, not to mention the extra no-wake-speed ride time from the marina down the channel and back out to the lake.
You are independent. If your setup allows launching without assistance, you can go virtually anywhere.
Inexpensive Kayaks for fishing are made by numerous boat builders, in two general styles: sit-on-top (the most common) and sit-inside boats. Sit-inside kayaks are what most of us think of when the word "kayak" comes to mind. A sit-on-top is a lot more like a surfboard with a seat molded into it, but they are very popular.
Sit-on-tops have a lot of virtues. Most are relatively inexpensive and easily available. They have nifty dry hatches and some have built-in live wells and bait wells; they come with integral rod holders, some have mounted swiveling rod holders, and a few have innovative hands-free foot-operated propelling mechanisms. Sit-on-tops are virtually impossible to sink, are wide and stable, and easy to climb back onto if you fall off.
The drawbacks? You are wet. There is no "freeboard", so waves and wakes will splash you. In cold water and cold air a wet-suit or a dry-suit is necessary. They tend to be heavy, since they're made most often made from blow-molded polypropylene, and need inside supports or a thick skin to stay rigid. They have scuppers (places for water to drain) so water will not accumulate in the boat, but scuppers, the way all I've seen are designed, introduce large, speed robbing dents on the underside of your boat. Remember that fast racing boats always have a glass-smooth streamlined hull. When you paddle a sit-on-top you are using a lot of energy just to overcome the lack of streamline on the hull. They are definitely not competitive for fast travel.
Sit-on-tops are therefore most popular where the water is fairly warm, and where the paddling distances are short. (Some manufacturers have tried to overcome the paddling difficulty by engineering foot-driven paddles, or by adding electric trolling motors, but either of those complicates the matter in my humble opinion.)
Sit-inside boats keep you dry by design, unless you tip them over. They have a full deck fore and aft, your legs fit underneath the deck in front of you, and you often wear a spray skirt so you are essentially waterproof inside the boat. They do not have scuppers, because water is not supposed to get inside the hull. They are beamy (wide) compared to similar touring kayaks, so stability is higher, but if you do tip over and fall out, you need to be experienced enough to know how to climb back inside and pump out the water. Sit-inside boats are often lighter, since there are not so many features molded into the hull shape, and the better designed sit-insides are available in wood (custom or semi-custom), hand-laid fiberglass, and even Kevlar (a high-strength synthetic fiber), rather than molded polypropylene, shedding additional weight (but costing more).
Sit-inside boats will be faster and easier to paddle, even if the same beam and length as a sit-on-top, since there are no speed-robbing drain holes in the bottom of the boat. Since they are often narrower and longer, sit-insides are also faster by design (a longer narrower boat will always be faster and go straighter than a shorter, wider, boat).
You can find a purpose-built sit-inside fishing kayak with many of the features of the sit-on-top boats: waterproof hatch covers, built-in and swiveling rod holders, even bait wells, but to keep perfectly dry you also need to add a spray skirt to keep water out of the hull and off your lap. You can also fish from a sit-inside in cold water on a cold day without a wetsuit--I do--since you are not getting splashed. In the rain or wind I add a fly fisherman's short wading jacket over the spray skirt and under the life jacket.
Related Post: What You Need to Know to Buy a Kayak