Nearly every engine renders the game in tiles, which is what we're trying to say. In order to achieve something more natural you have to plan your tiles to be more natural, and a square and boring level is only hindering you in that. Imagine up a more lively level, start building, and make your tiles as you need them rather than just making your tiles and building what you can with what you made. You simply have to make more diverse tiles.
For example, here is a screenshot from Zelda: Link to the Past.
They use tiles, but look at the dirt and the grass and swamp... it's not laid out in squares. Instead, they use their tiles to their advantage to make things more natural and round. Now, admittedly, 32x32 is large for a tile which means they won't be as flexible, but you can remedy this by making more combinations. Instead of simply having one tile for the flowers, make two or three with the flower in different positions in the tile, or with different amounts of flowers. Instead of making just one sharp corner tile for the dirt, also make a more round corner tile, and combine the two to make a more natural path. Really, this comes down to a combination of level design AND graphical design, and you can't approach both independently.
