Are there any planes that have ramjet or scramjet engines?
Scramjets
There's only a couple flying examples. The early Soviet-born Kholod, the HyShot series, and the recent ISRO ATV all flew small scramjet engines, although none were designed for net thrust. By far the most [publicly] successful vehicles have been the X-43A and the X-51. Both were fully controllable, independent flight vehicles (rather than just engines hanging from rockets) that produced net thrust.
The NASA X-43A hypersonic research vehicle was dropped from a B-52, then boosted by a modified Pegasus booster, and briefly flew at Mach 9.6 with a hydrogen-fueled scramjet.
 
Credit: NASA

Credit: NASA
The Boeing X-51 Waverider hypersonic research vehicle was also dropped from a B-52, then boosted by a modified ATACMS (an Army surface-to-surface missile), and then flew at Mach 7 with a JP-7-fueled scramjet.

Credit: USAF
The DARPA Falcon program aimed to produce a hypersonic plane that could takeoff and land under its own power using a turbine-based combined cycle (TBCC) propulsion system (NASA TBCC overivew on NTRS). Two early designs, HTV-1 and HTV-2, were unpowered hypersonic gliders, the latter was launched by ICBMs (basically reentry vehicles, like the X-41 they were probably derived from). But the next two designs, HTV-3X Blackswift (YouTube) and the final Hypersonic Cruise Vehicle (HCV) (YouTube), would have been the first reusable, hypersonic CTOL aircraft. HCV would have been able to carry a few thousands pounds of payload (eg bombs, flight test equipment, cameras) very quickly across great distances. The [HTV-3X and HCV] program was eventually canceled, but other work continues on hypersonic weapons and vehicles.
 
Credit: DARPA
SR-72. Lockheed Martin is developing the SR-72, an unmanned Mach 6+ ISR (recon) platform. It's meant to fly completely under its own power using TBCC, taking off with turbines and transitioning to ramjet and finally scramjet operation. A key innovation was bridging the speed gap between where turbojets stop working well and where ramjets start working well, but LM declined to elaborate how they achieved that. Their design apparently builds upon their work on the Falcon program (see above). They said they'd fly a single-engined demo before moving to the twin-engined, full-scale vehicle.

Credit: Lockheed Martin
Other ambitious unflown designs include the LLNL Hypersoar and the X-30 National Aerospace Plane. Both were large (100-200 tonnes MTOW), hypersonic, intercontinental vehicles. The SSTO-capable X-30 could launch payloads to LEO as well as serve intercontinental passenger routes. Hypersoar was also envisioned to carry passengers in one variant, perform TSTO in another, and also perform global strike/recon in yet another.

X-30 NASP. Credit: Chad Slattery

Hypersoar. Source: FAS.
Ramjets
The Republic XF-103 Thunderwarrior was essentially an early attempt at TBCC in a manned interceptor. It was a very innovative design (Mach 3-5, no canopy, periscope, crew capsule, huge radar, and internal bays for 6 large missiles, precursors to the AIM-54) but never flew.

Source. Unknown.

Source with lots of great background.
There's a variety of ramjet powered missiles
Notable examples include...
... the Bomarc. Credit: Boeing.

... the GQM-163 Coyote, a notable supersonic, sea-skimming target. Credit: DR Kirk.

... the massive P-700 Granit Source and its relatives, the P-800 Oniks and the BrahMos.

... the RIM-8 Talos SAM. Credit: USN.

... and the Sea Dart, the Moskit, the Hughes/Raytheon AIM-152 (and related ACIMD), the Triple Target Terminator, and a bunch others. Some are antiship missiles (various trajectories), some are SAMs, and some are air to air missiles. All were rocket-boosted before the ramjet took over.
Obviously the most &quot;terrifying&quot; was the Supersonic Low Altitude Missile of Project Pluto fame, a nuclear-armed, nuclear-powered ramjet for the 100,000 mi cruise missile. Air was blown directly through the reactor, directly heating it for thrust. Its unshielded reactor would have propelled it to Mach 3+ at sea-level and irradiated targets below it before crashing into a final target, irradiating that as well. They successfully tested two engines before the program was cancelled in favor of ballistic missiles.
Here's a fun USAF-Convair vid from 1959 explaining the concept:

                
            
 
Credit: USG