Our school district has alternate day kindergarten (full days on mon/wed and fri morning or full days on tues/thurs and fri afternoon). That is free. There's also the option to pay for full-time. Most parents send their kids full time. We sent our son full time 2 years ago. Many of his friends went alternate day... some are in the gifted & talented program with him now. If you look at a typical 2nd grade classroom, you can not tell which children went full time and which went alternate day. They have the same curriculum and learn the same stuff. The only difference is that the full time kids have more opportunities in the classroom to reinforce what is learned and practice it.
As for the reasons... many of our friends who do alternate day do it for financial reasons. They also want to spend another year with their children doing things like zoo trips, hiking, playgroups, children's museums, etc before entering 1st grade. Once the kids start going fulltime it's really hard to fit those type of things into the schedule (and those places are packed on weekends). Some of the kids also do other programs like weekly classes at the children's museum or soemthing like that, that is also educational and social.
Our reasons for sending our son full time was pretty simple: he needs a routine. He not just thrives on it, but his personality pretty much demands it. Going to school every other day would've been a disaster. As it is, weekends can get messy because they are different. This is very typical of ADHD and Asperger kids, though.
Just as a side note... we are the only school district in the area with this schedule. Most go everyday for half-days. Although most also offer full day, everyday. I think the consistency is better.