This has been my theme for the uncommonly warm Connecticut winter of 2011-2012. Starting with a severely over taxed trailer trundling home a curb found sleeper sofa, climaxing with a polyamorous Bike Move, and lingering on pleasantly with various solo cargo and free cycle pickups.
The right equipment helps. You can carry a surprising amount with a rack on a standard bike, and a little bit more with a cargo specific bike, but if you really want to push the limits you'll need a bicycle trailer of the sturdy variety. Preferably something with a rigid deck, lots of tie down hooks, and a raised platform of sorts to allow wide loads that would extend beyond the wheelbase. The hitch needs to be sturdy, and attached in a way that won't rotate under load (and inta yer spokes).
A couple years ago I modified a Trek two-child trailer with a piece of plywood and a 40 gallon Rubbermaid. The Rubbermaid bin acts as both a weather tight container and a raised platform for wide loads. The modification was easy, and done in a single Saturday afternoon. Nearly the perfect little cargo trailer, the only flaw is the hitch. It's a cam locked strap around a pair of rubber coated clam shell pieces. If not clamped super tight on a round chainstay it will rotate when the trailer is heavily loaded. You'll see that for heavy loads I've augmented the clamping friction with a used bicycle tube.
Now on to the question of import, "What can't you move with a bike?" Definitely not an elephant. Maybe a small cow. Seriously. Some things lend themselves to bike transport more than others. First, you've got a weight limit. I've had ~200 lbs on my wee trailer, but that's getting to it's hairy edge for capacity. When towing upwards of 100 lbs, everything needs to be perfectly balanced. Now some trailers are designed with heavier duty hitches and frames. Our illustrious Interstatement has one of these monsters - and that officially gets you up to 300 lbs, unless you blow an o-ring. Interstatement's heavy duty Bikes at Work trailer was utilized to move my full size sleeper sofa.
There are also structural considerations when moving a load using a bicycle rack or trailer. Big floppy stuff is hard to move. Rigid things that can be stacked or non-rigid things that can be stuffed into Rubbermaid bins (see photo below) that then can be stacked are much easier to secure. A fist full of bungee cords combined with one or two non-stretch load straps are usually enough to tie down a load. I've carried loads on my small bike trailer that wouldn't fit into a typical SUV or your typical car trunk. I grin smugly at passing, empty, single occupant SUV's when transporting large items with my bicycle. Ha!
Here are some photos from my recent bicycle move from East Hartford to downtown Hartford. Part of the move was with friends, but a good portion was solo trips over a couple of weeks. A mid-week laden bicycle trailer was even the subject of some security department scrutiny at work. I guess parking a bike trailer with a bike and bicycle frame strapped to the top could be misinterpreted (or correctly interpreted?) as a threat to Joe Lieberman and the greater military industrial complex. Bikes Not Bombs, kiddos.