Non FTL interstellar travel is possible, look at the voyager/pioneer probes. Even a technological backwater like the earth can send objects interstellar, without really trying or setting out to do so
Note: We are talking interstellar in only its most literal sense, the probes will be so much space junk and we'll all be long gone by the time they arrive anywhere.
Looking at non FTL technologies speeds of between 10%, 25% and even 50% speol(c) should be achievable. Indeed none of the technology required for this is that radical, given the finances and the political will we could send a functioning probe interstellar. Projected journey times to Alpha Centauri were between 42 and 46 years. (Figures quoted were for Project Deadalus - a WWW search will provide any details required), quite a long time, but given the length of time space missions go on for at present, it's not really that long. The Cassini probe, for instance, will take seven years to reach Saturn.
So what are the technologies that will allow us to reach for the stars ?
The Project offered to use nuclear bombs for space travel. About 5 bombs per second are dropped out the back and detonated to propel the craft along. A huge shock plate with shock absorbers make up the base of the craft. Experiments using conventional explosives were conducted to demonstrate the viability of this scheme. Although this vehicle was originally conceived to take a crew to Mars, it can also be considered for sending smaller probes to the stars. This project ended with the nuclear test ban treaty in the 60’s.
The British Interplanetary Society revisited the Orion propulsion concept, but at a more reasonable scale and for in-space use only. Project Daedalus was a design study for sending a probe past Barnard’s star with a 50 year trip time. (Barnard’s star is about 6 Light Years away.) It would have been driven by fusion "microexplosions" caused by irradiating fuel pellets with electron beams at pulse rates up to 250 Hz, in a magnetic "combustion chamber". Confinement and shaping of the plasma with a magnetic field would make Daedalus vastly more efficient than Orion. Daedalus would work just as well in the solar system as between the stars, and one can imagine that in 75 to 100 years fusion freighters will be sailing regularly between the planets. An important point is that no one has yet produced controlled fusion energy with electron beams or anything else, while the technology required to build an Orion-type spaceship has existed for over thirty years. Nuclear propulsion will get into space eventually. Orion/Daedalus might be the device that makes possible human occupation and economic exploitation of the solar system. As an aside the Shiva Nova Laser project may throw some light on the subject of controlled beam powered fusion. Though not electron based, or even vaguely portable, the research being done could prove to be applicable.
Well, rather than bring your fuel along, why not get it as you go. This Bussard Interstellar Ramjet concept, from the 1960’s, relies on scooping up the lonely protons that drift in interstellar space, and then somehow getting them to fuse to make a nuclear rocket. There are a variety of limitations to this concept, such as how many protons can be scooped up, the drag created from scooping them, and, not to mention, the feat of getting these protons to engage in nuclear fusion for a rocket.
Light sails are another possibility. Rather than use rockets, why not use light. When light strikes an object, it pushes on it ever so slightly. Use lots of light over a very large area, and the forces get noticeable. That is the idea first proposed by Robert Forward. proposed using a powerful Laser to shine through a thousand kilometer Fresnel lens onto a thousand kilometer sail. With this kind of setup, it is claimed that one could send a thousand-ton vehicle with crew to our nearest star in 10 years!
So, these light sail type devices being pumped by high powered lasers could get to about 50% speol(c). The problem with these devices however would be turning and slowing down. You'd have to use the Stellar wind of the target system to slow down. Plus light sails would be a tad delicate, for interstellar travel. Also imagine the size of the laser required. Forwards original ideas would have required a Laser producing 10-million-gigawatts, this was later revised to a microwave laser of a mere 10-gigawatts.
Having said this light ships/sails already exist. A scientist called Leik Myrabo has managed to get a foil disc airbourne for a short period of time, to a height of about 20m, totally propelled by light, its not much, but its a start. The idea is eventually to be able to put these devices into orbit. They'd by able to carry very small and light instrument packages, for scientific/military purposes.
R. Forward - http://www.whidbey.com/forward/
G. Landis - http://www.aleph.se/Trans/Tech/Space/laser.txt
Leik Myrabo - On Wings of Light - http://www.newscientist.co.uk/ns/980110/features.html