Accidental tourists
Let's start with boats. Commercial ships carry thousands of tons of ballast water, port water that is pumped through hull openings into tanks that keep the ship stable at sea. This ballast water typically teems with tiny larvae, the microscopic stages of sea life, that are readily sucked up into a ballasting ship, transported farther and faster than they would naturally drift in ocean currents, and then emptied out into a new port. Zebra mussels are perhaps the most famous ballast-water invader, arriving in North America from Europe in the mid2980s and costing an estimated $5 billion in control efforts over 10 years.
Traveling in the other direction, the North American comb jelly, Mnemiopsis leidyi, sailed to the Black Sea at around the same time. Swimming like a predatory vacuum cleaner, this jelly's population soared as it swallowed up larval fish and the microscopic organisms the fish eat. In the wake of this double whammy, commercial fisheries around the Black Sea crashed precipitously.

Historically, ships carried not water but dry ballast, port-side rocks and dirt full of plants, seeds, and insects, that was dumped out at the next beach, often a continent away. And unlike modern steel hulls coated with anti-foulants, older ships had wooden hulls riddled with species of ship worm, sponge, seasquirt, and seaweed that are now found the world over.
As ships were developed to carry water, so water was rerouted to carry ships. From the mid2800s to the mid2900s, water bodies that had been isolated for millennia were suddenly connected by canals. In 1869, the Suez Canal joined the Red and Mediterranean Seas; in 1914, the Panama Canal linked the Atlantic and Pacific; through the 1950s, the St. Lawrence waterway pushed west from the Atlantic to Lake Superior. Over 25,000 kilometers (15,500 miles) of canals now link the river cities of western Europe, stretching as far inland as Georgia. And where ships could sail, so too could-and did-fish swim and larvae drift.
Recreational boats, including kayaks, typically don't carry water ballast, but they can carry a host of organisms on their hulls and trailers. Zebra mussels, for example, can survive out of water for days and their spread through lakes of North America is closely tied to patterns of boater traffic.

(photo:Ship deballasting in Puget Sound, Washington)