I'm really intrigued by all the amazing bridge architecture and designs people come up with (for example: Lego Cable Stayed Bridge) and it got me wondering, do larger structures like that need any form of adhesive between the bricks? Are bricks (in general) strong enough to hold larger structures on their own?
Such structures in LEGOland parks are usually reinforced with a metallic structure hidden within the model. And they use glue. No wonder LEGO sold them away.
Some fans do use similar tricks, I've seen some make trees by embedding a wooden skewer in a trunk of 1x1 round bricks. Without that, the tree would collapse too often, and that's not even a large structure to start with. (Purists would use rigid 3mm LEGO hoses)
For a pure LEGO structure, in any case you would need to make sure not to rely on clutch power only, but I suppose you guessed as much already. As stack of 1x2 bricks won't hold, a length of interleaved 1x2 plates will be sturdier. Depending on the length, you'll need more layers, but that's about it.
I doubt adhesive would help that much — glue maybe, but let's not go there.
There`s the question "How much weight can a handle of Technic pegs and beams support?" covering the principles for structures. You can find a mechanical stress study right here.
For building anything of normal Lego size, the bricks generally stick together nicely if you overlap your bricks during construction. If you are making something of great size, walls of 2 or 4 dots using an overlapping pattern will produce something quite strong.
Because of the shape of Legos, they are weakest when pulled from the bottom. They are designed to rely on Gravity for strength, not to work against it. So, if you move something heavy, the bottom of the model must be supported or a portion of it will likely pull loose.
And of course, if you are building something permanent, like in Legoland park, the suggestions above to glue and support the internal structure are valid. But for typical home use, it is unnecessary.