The following passages offer unconditional prophecies. You might not agree with every single one of them, but you might also deem most of them to indeed be without any plainly implied conditions.
Israel will be enslaved by Mitzrim for 400 years, then be brought out with the plagues due to the iniquity of the Amorites (Gen 15:13-16)
Abraham's offspring will obey (Gen 18:17-19)
Israel will turn away after Moses' death (Dt 31:16, 32:15-18)
Ishmael's blessing (Gen 16:12, 17:20)
Pharaoh will not let Israel go but will after the plagues (Ex 3:19-20)
Mitzrim will favor the Israelites and shall give riches to Israel (Ex 3:21-22)
The exodus would occur at that time, for that generation (Ex 6:6-8)
Moses' blessing on Israel (Dt 33)
7 years of famine (Gen 41)
I do not think that the idea of an unconditional prophecy or foretelling of the future would present a problem for personal responsibility. In a sense, I think hearts can be hardened or softened and that is also indicated by the text when Pharaoh's heart is hardened. Did that take away his free will? Maybe, maybe not, in a sense. When Abraham was told that those things (blessings, etc) would certainly happen, I doubt it changed his resolve to be obedient. I think someone who is indeed sincere would not take occasion at something like that to then disobey.
Gen15:13-16 - God - any type of prophecy (conditional and unconditional)
Gen 18:17-19 - God - any type of prophecy (conditional and unconditional)
Dt 31:16, 32:15-18 - God - any type of prophecy (conditional and unconditional)
Gen 16:12 - Messenger of God (Malach Yahweh) - any type of prophecy (conditional and unconditional)
Ex 3:19-20 - God - any type of prophecy (conditional and unconditional)
Ex 3:21-22 - God - any type of prophecy (conditional and unconditional)
Ex 6:6-8 - God - any type of prophecy (conditional and unconditional)
Dt 33 - Prophet (Navi) - Only conditional prophecy.
Gen 41 - Dream (Chalom) - Prophecy comes from God (see Gen 41:16) so any type of prophecy (conditional and unconditional)
So, save for the one passage, all of those prophecies have both conditional and unconditional components.
For example, Genesis 22:1 is an example of a conditional prophecy from God. Its says so explicitly in the text (nisa). So even though Abraham was probably inclined to obey God anyway, it was up to his free will to either fulfill the prophecy or not.
Or for example Joseph, when he predicted the future of his cell-mates. This was an example of an unconditional prophecy. Because his cell-mates had no control over the situation.
However, when Joseph spoke with Pharaoh it was an example of a conditional prophecy, because it was up to the Pharaoh to obey or not. Pharaoh has control over the situation.
So prophecy can take either form, except for the Prophet. Prophet must prophesy conditionally so he can be tested. For example, even Moses prophesied conditionally. I.e. Deut 11:26-28