I myself am using grass clippings. I've heard some say that they will grow grass in your garden, but I haven't found that to be the case. I lay them on top of my garden, and then I don't till the rows till fall.
The tilling issue when you have a mulch is really the reason why I don't put it over my entire garden. You see, my garden is so wide that I can't help but to walk down through the rows to tie, prune, and harvest. By stomping around, I end up compacting the soil, so I in turn till (hoe) the paths in-between rows 3 or 4 times a month. If I mulched the rows, I'd still have to till them to fix the damage I do by trompsing around in there. But....the tilling would disrupt the mulch, thus defeating the purpose. So, this year I'm going to mulch where I don't walk and till where I do.
How do you guys handle the mulch/hoe issue?