As far as early changes go, you won't see too many, since in a lot of ways crossbows were very similar to early guns -- they reloaded just as slow, so volley fire was still important (though they were very accurate, I believe moreso than primitive firearms). As people have mentioned, artillery is the most important.
I just had an idea about people besieging a castle and using acidic compounds to burn down the walls. Now, that'd be cool... In fact, chemical warfare may be more widespread in general. With a catapult or trebuchet you may not be able to punch down walls, but you certainly could launch a canister full of poison over walls -- this happened OTL (including such things as launching rotting corpses over the walls to cause infections), but seemed to lose popularity as castles did, as far as I know (correct me if I'm wrong).
Professional armies will probably last longer than OTL, though not too much longer, especially when someone figures out its a lot more cost effective to give 1,000 peasants crossbows than 100 knights a full suit of armor, a horse, and so on...
The impact on naval warfare is huge. I'm... not even really sure how it was prosecuted before gunpowder was invented. Arrows, then boarding?
Another important thing is to consider the non-military aspects of explosives, such as construction, clearing land, etc... Of course, I think by the time this comes around, people will have discovered some other sort of explosive (or gunpowder, or whatever). The fact is that there are a lot of chemical compounds out there that explode and people are eventually going to find them.