Yes, Padua has canals like Venice and Treviso. It used to have even more but many have been covered over to create roads. For example, about 20 years ago a road was named Riviera Tito Livio, near my place of work, recalling its origin as a water route. In the past, water was the best way to transport people and goods from city to city so even the inland city of Padua built a series of canals, mostly to connect it with Venice, which opens up to the lagoon and Adriatic Sea. But now cars and trucks seem to transport just about everything so roads are necessary and Padua's waterways are mostly explored by foreign tourists and local canoe clubs.
This particular boat, or burchiello, leaves from the Piòvego in the city centre, within a few minutes' walk to the train station.
There are several boat services of different shapes and sizes that take their guests through Padua, around Padua and along the Riviera Brenta to visit several important Venetian villas such as Villa Pisani, Villa Widmann, Barchessa Valmarana and Villa Malcontenta or from Padua toward Battaglia Terme to see the villas and waterfront of the Euganean Hills and Monselice. You can find trips for all tastes and price ranges, with time-frames ranging from one hour, half-day to full-day varieties. Here is a list of them:
And if you decide to go a trip now with them, you might be able to take advantage of their low-season rates! (July and August heat seems to be a deterrent for some, but on the other hand, you won't have to worry about rain!)