There are two must-have articles for every website about photography: "What's in my bag" and "How to clean a DSLR sensor". The first is a problem for me, because I have three bags of different sizes..;-) But anyhow I can tell you something about my way of sensor cleaning.
My tools for cleaning sensors: The first is my pocket air blower, the second is - not joking! - my vacuum cleaner (nicknamed R2-D2).
If I notice specks on my sensor I first try to blow them away with my pocket air blower. Remove the lens, say "mirror up" in the camera's menu and hold the camera with the mount downwards. Then blow a few times through the mount and check if the specks are off by photographing a uniform subject like the sky well stopped down. A perfect demonstration of this is given by Jared Polin on youtube.com. Of course, I can do this sort of cleaning even in the field if necessary.
R2-D2 at work!
If some specks remain, I activate my R2-D2. I set it to a low level and put the camera body on the floor with mirror up and open shutter. Then I hold the end of the vacuum cleaner hose about 1cm above the mount and vacuum for about 15 seconds while moving it slightly back and forth. Pay attention: don't move the hose through the mount, otherwise your camera loses some weight but will no longer be a camera! And it is very important that you fix the camera body on the floor with your other hand while vacuuming, because there is the danger that your vacuum cleaner - if it is a good one - lifts up the camera.
After this procedure check if all the specks are gone. If not, repeat it!
BTW: I can definitively tell you that this tool is not in my bag :-)
I've found this tip many years ago on the website of Ken Rockwell and since then I've successfully cleaned all my DSLRs like this. Until now, R2-D2 has failed only once, that was on my D700 after about 50000 shots...
No, I don't wipe my sensors! If my R2-D2 was not able to clean the sensor I ship the DSLR to the Nikon service. Nikon Germany offers an inspection of your camera including sensor cleaning for 49.-€ if your camera is registered (otherwise it's 79.-€). The one time it was necessary for my D700, they did a great job.