It's near certain that other Bitcoin-like currencies will continue to be introduced from time to time. Some of them will likely gain some traction.
Over time, more and more deficiencies of Bitcoin will become apparent and newly-designed competitors will be able to fix them. While Bitcoin can certainly make some changes, it will always have a trade-off because significant changes risk shaking to confidence of current users. At some point, Bitcoin's accumulated deficiencies will be too much and it will lose significant share to some competitor.
Of course whether that will be next year or next century, I don't think anybody knows.
Some such systems will likely coexist with Bitcoin without much interaction. Others may design in interaction with Bitcoins directly into their fundamental design. Nobody has a crystal ball though.
Some have imagined high-speed, high-volume systems that would move Bitcoins outside the regular blockchain with the existing Bitcoin system used only to "settle up" large transfers between smaller, faster systems. Will that be what happens? Who knows?