Reason #1: Combines both physical exercise and meditation. Paddling gives you a great upper body workout and good cardio exercise. It also allows you to let your thoughts wander and mull over life while you are rhythmically stroking your paddle into the water.
Reason #2: Back to nature. Allowing yourself to slow down and drink in all that nature has to offer is a real blessing in my book. Getting up close and personal with a blue heron, watching a sun rise or set, and looking at the beauty of towering trees reflected in the still waters... are all big pluses to kayaking.
Reason #3: Solo versus tandem. You can kayak with a partner or go solo. Two different experiences - both rewarding. Tandem kayaking allows you to share your experiences with someone else and chat together. Just be sure you are both "stroking" together or you will get out of rhythm... and that kayak will not go anywhere! ;-) If you tire of too much togetherness, then there is always going it alone. More meditation opportunities and you get to paddle where "you" want to go! :-)
Reason #4: It is relatively cheap. For under approximately $500, you can purchase a used kayak, paddles, life jackets, and some kind of rig to haul it to the water. Especially if you are into the more leisure side of kayaking, you don't have to invest your life savings here. Shop around. Maybe rent one for the first few times to get a feel for the kayak and what you would like long term. Check out the various articles and links on my blog for tips on purchasing your first kayak.
Reason #5: It is simple. No motor, no sail (unless you are into sea kayaking), no rudder (usually), and no huge trailers. Many kayaks are relatively light weight - my Mainstream Escapade tandem kayak weights just 65 lbs and can be handled by one person.