There are several alternatives to renting a wood chipper for disposing of limbs and branches, but none do as thorough a job as a chipper.
If the issue is simply cost or reluctance to use a chipper, considering using a community chipping program. Many communities and cities host programs where homeowners can simply take their wood to a public lot. City employees then chip the wood and either offer the homeowner the resulting chips for mulch or use it for mulch in city parks. To find out if your community participates in such a program contact your city’s park department and ask.
It’s hard to beat a wood chipper for quickly and easily disposing of large tree limbs. But for many reasons, noise, expense, availability, safety concerns, space etc. many homeowners look for an alternative to the chipper. The primary alternative to chipping the wood is cutting it up with a chain saw and/or wood splitter and stacking the wood for burning—either in a fireplace or brush pile. For small limbs it’s possible, but very labor intensive to use an axe and hatchet to chop limbs into manageable sizes for composting. If you just have leaves and small twigs and branches, a shredder can be a good alternative to a chipper. A shredder can quickly turn leaves and twigs into mulch. A power lawn mower can be used for mulching leaves, but not twigs, branches or wood.