Upvote:2
Some self-storage places, and mailbox services, offer this type of service. However, they are rarely geared up to handle delivery to multiple countries, so are of limited use for travel.
Examples for smaller packages include Storage by Mail and Ship 2 Storage. For larger amounts up to house size there's people like Flexistore (UK), uBox and Pods.
Probably the best way is to leave the packages with a relative or friend, and get them to ship them to you if needed. Alternatively, a local mailbox and shipping place in your home country could be another option, if they're flexible enough to just keep a few boxes in the back room and ship them to you worldwide on demand.