Faster-than-Warp - Successes
- VOY: The Gift - Kes' Powers
- VOY: Night - Spatial Vortex
- VOY: Timeless - Quantum Slipstream drive
- VOY: The Voyager Conspiracy - Quantum Catapult
- VOY: Dragon's Teeth - Subspace Corridors
- VOY: Q2 - Q-Powers
- VOY: Dark Frontier - Stolen Borg Transwarp coil
- VOY: Endgame - Borg Transwarp corridor
- VOY: Death Wish - Q-Powers (not sure where they went, but presumably to somewhere Christmas Trees are a thing)
- VOY: Future's End Part I - Graviton distortion (okay so they turned up in the 1990's but they still made it to Earth)
Faster-than-Warp - Failures
- VOY: Caretaker - The Caretaker's displacement wave technology (decided to destroy it instead)
- VOY: Eye of the Needle - Wormhole (too small, oh and it went to the past)
- VOY: Prime Factors - Sikarian Spatial Trajector (didn't integrate with Voyager's systems, and limited to use near Sikaris)
- VOY: The '37s - Briori technology (the revolting human slaves had already destroyed it before Voyager got there)
- VOY: Cold Fire - Nacene technology (they detected Suspiria's presence hoping she would send them home, she wasn't happy to see them)
- VOY: Day of Honor - Attempt to upgrade Voyager's engines to use transwarp tech based on Seven's Borg knowledge (tachyons flood the warp core and they're forced to eject it)
- VOY: Threshold - New "Warp 10" engines (it worked, sort of, minor side effects may include turning into lizards)
- VOY: False Profits - Barzan wormhole (both ends of the wormhole get unpinned during the kerfuffle rendering it useless, didn't they warn them about Ferengi at the academy?)
- VOY: Death Wish - Q-Powers (Q offeres to return them home if Janeway goes his way in the hearing, she declines)
- VOY: The Q and the Grey - Q-Powers (Q offers Janeway an Indecent Proposal, she declines)
- VOY: Inside Man - Geodesic fold (it would have gotten them back, minor side effects include certain death)
- VOY: Equinox - Enhanced warp drive (Janeway declines to use it given it runs on killing sentient aliens)
- VOY: Future's End Part II - 29th Century technology (Janeway asks Braxton to return them to the Alpha Quadrant, he declines under the Temporal Prime Directive)
Faster-than-Subspace - Successes
- VOY: Message in a Bottle - Hirogen relay network (used to send the Doctor to the USS Prometheus)
- VOY: Hunters - Hirogen relay network (used by Starfleet to send messages to Voyager)
- VOY: Pathfinder - MIDAS array (used by the Pathfinder Project to communicate with Voyager)
- VOY: Lifeline - MIDAS array (used by Voyager to send the Doctor on a housecall to Dr. Zimmerman)
NB: There are other instances of the Pathfinder project communications but they're minor "new letters from home" ones once regular communication has been established, I think this is all the major plot-driving ones.
Faster-than-Subspace - Failures
- VOY: Eye of the Needle - sending messages the "long way" via giving them to the Romulan captain in the past and having him relay them in the "present" (unsure but the Romulan dies before Voyager is stranded so it's unlikely they were delivered)