When the wind is blowing around 15 knots, I usually do other stuff (mow the lawn, put in a few extra hours at work, etc) to clear my schedule for when the weather is nicer. However, I have fished and caught fish when it was blowing over 15. Things I consider before I go:
1) Orientation of the place I want to fish. Some spots offer protection even at almost 20 knots.
2) Water temperature. 15kts+ isn't bad when the water is 80 degrees, but it's a different story when the water is 60 or less.
3) Tide. If the tide opposes the wind, the waves will be bigger.
4) Forecast. I've launched in 15+ wind lots of times because I had a feeling it was going to die down later in the day. Usually, it works out. In contrast, I'll hesitate to launch if it's calm but forecasted to get windy later.
5) How I feel. Sometimes I'm up for an adventure, sometimes I'm not. If I've been having a string of bad luck or I'm feeling tired or foggy, I'll keep off the water.
6) Quality of the fish. If it's been hot lately, I'll be more inclined to launch--also if it's been a while since I've last fished. If the fishing hasn't been great, and the forecast is iffy, I'll be less inclined to go.
I think that sums it up. 15kt is generally my cut off, and I always try to err on the side of caution.
Ditto to anything Ictalurus wrote.
If I add, I fish in the rain as long as there is no lightening and the wind blows below 10MPH. I fished every weekend on the salt waters this year when I did not have do chores whether I was at home or away until the last weekend. Being very mobile as a kayak-fisherman, I managed to find the protected waters all the time. Though, the last weekend, the fishing for not-so-quality fish was not really worth 2 hours of driving (one way) to the Bay. So I changed the destination to a local reservoir for Bass. I did not catch any. I did not have lures for the fresh water in my tackle bag.
BTW, Was the bay really rough last weekend? If the bay was calm, I will be upset.
The worst I ever got caught out in was this one day, and the fishing was amazing. I could have easily gone with the wind to the near shore if I needed to, but I have found that a kayak can slice through some nasty stuff if you can keep the bow oriented the right way. I'm not advocating a reckless approach, but don't panic if you get yourself in some nasty stuff. Yes, the video ends with the DNR coming to yell on me for being out there.