Many of the amps that have two input jacks, if you use both simultaneously, it connects the two source to each other in parallel. A couple things that'll do:
1) If one of the instruments is active, the other one (a passive instrument with a higher impedance) will be attenuated A LOT - you won't hear much of it at all.
2) If both instruments are passive, you might get way with it, but know that they will interact - if, for example, one of them has a standard volume control (a P bass, for example), and you turn it off, it will turn off both instruments. Turning it down, similar effects will happen. Switching from 1 pickup to 2 (in parallel), the other instrument (because your instrument now has a lower impedance) will get quieter.
In short, its not likely to cause the end of the world, and if your band is a few teenagers in the basement with nobody listening (intentionally - Mom and Dad probably can't help but hear you), then maybe it's OK, but it isn't something to consider in live performance - until the day one of your amps blows and you have no choice.
OH, and by the way, two guitars playing through the same amp, with tremolo - that's kind of a neat effect. But I wouldn't do it for more than one song, or the audience will get seasick.