There is a new common sense approach to infinity called 'Extreme Finitism' (see http://www.extremefinitism.com/).
The website has some interesting articles including an INVESTIGATION OF INFINITY IN MATHEMATICS (see http://www.extremefinitism.com/background/).
One article has the definitive answer to the question 'does infinity exist?' (see http://www.extremefinitism.com/blog/does-infinity-exist-the-definitive-a...).
This website takes a common sense approach, and so people who like the weird things made possible by a belief in infinity will be sorely disappointed.