Can aircraft other than rockets go to space?
Depends on what you mean.

Get to high altitude? Yes you can. It is really inefficient to get there, but some aircraft already do it.

Achieve a stable orbit and be able to maintain control? No, at those altitudes you do not have enough oxygen to keep your engines running, you have to bring your own (and thus use a rocket)



For the sake of clarity, some definitions:


reaction engine: includes both rockets and jets. The engine pushes some mass in one direction and by reaction it achieves thrust in the opposite one.
jet (engine): is used to refer to airbreathing engines. The aircraft carries the fuel, but not the oxidizer; that is taken from the surrounding atmosphere.
rocket (engine): is used to refer to non-airbreathing engines. The (space)craft carries both the fuel and the oxidizer. No atmosphere is needed.
space: above 100km of altitude.
go to space: 

staying in space:

Images from xkcd