The first step in spaceflight is to get off the Earth, and Comparison of orbital launch systems - Wikipedia is a good reference for the rockets developed for getting into low Earth orbit (LEO) and beyond.
However, the active systems max out at a little over 20 metric tons to LEO: US Delta IV-H, EU Ariane 5 ES, Russian Proton M. That is also true of the US Space Shuttle and the US Titan IV-B, both decommissioned over the last decade. The ones with greater payload have been one-off so far:
- NASA Saturn V: 118 mt to LEO -- Apollo and Skylab. The last three Apollo missions were canceled and some of their hardware reused for other projects.
- Soviet Energia: 100 mt to LEO -- only one flight, with Buran space shuttle.
- Soviet N1: 95 mt to LEO -- four flights, all failures. Intended to send cosmonauts to the Moon.
The US has two systems in development:
- SpaceX Falcon Heavy: 53 mt to LEO -- should have some test flights this year. Two payloads lined up for it.
- NASA Space Launch System, successor of Ares I and Ares V. Block 1: 70 mt to LEO, Block 2: 130 mt to LEO -- in development for Orion return to the Moon. First flight proposed for 2017.
The Falcon Heavy will use 3 Falcon 9 first stages side by side, and a Falcon 9 second stage. That's expected to lower its launch costs compared to a one-off design.
The SLS will use first-stage engines and solid rocket boosters derived from Space Shuttle designs, much like Ares I and Ares V.
It seems to me that the Falcon Heavy is likely to enter service, but that the SLS risks the fate of Ares I and Ares V: cancellation before any launches.