I mostly use my eyelead, but it sometimes doesn't get stubborn debris out of the corners of the sensor where I maybe can't get it completely flat against the sensor, so I bought some swabs and eclipse fluid which helped. I find that using the swabs, I do often get small random bits of dust or debris on the sensor afterwards, and a quick dab with the eyelead afterwards does the trick.
I mostly shoot motorsport photography, and will change lenses (or mostly add a 1.4x extender) 15 - 20 times during a day in a far from pristine environment, so dust on sensor is very common. I only clean my sensors about once every 3 months though, as for the most part I can live with the odd small spot that is easily cloned out in the sky or corners.
I too use Eclipse cleaning fluid with swabs. 