When reading through the law in the Old Testament it seems that there are only sacrifices for unintentional sins. Is this true? How does the New Testament handle intentional sins such as drunkenness, lust, bad habits, etc? And, how does the Old Testament deal with these sins as far as forgiveness goes?
The Old Testament is clear that only unintentional sins can be atoned for:
The idea of 'intentional' is better understood as 'defiant' or 'high handed'. Unintentional therefore includes many sins committed due to want of knowledge, through weakness, or where the offender did not really understand his guilt. Intentional sin, is not that you were consciously aware of sinning, like when King David committed adultery, rather it is more of a public defiance against the covenant, like the man stoned for picking up sticks on the Sabbath (Num 15:32), just after God had declared that the whole camp should not work on the Sabbath. This open rebellion during the establishment of the ceremony was like a spirit of mutiny on a ship at sea. This is what 'intentional' means in this context.
The punishment of 'cut off' is understood differently by various ancient and modern commentators. However as many 'high handed' sins were punishable by death, the term should not be confused with excommunication as some sins incurred but as in literally being put to death. Naturally their is no atonement for that.
In the New Testament this 'cutting off'' is referred to in three ways.
First as 'intentional sin' is actually open unrepentant rebellion to God. This has a corresponding reality in blasphemy against the Holy Spirit (Heb 6:4).
Second in showing when people commit great sins that seem like blasphemy but are not due to 'ignorance', such as Peter's sermon in Acts which implied many Jews killed Christ 'in ignorance' (Acts 3:17). Peter is saying, 'Even though it seems that you have 'intentionally' sinned when killing Christ, many of you did not actually blaspheme the Holy Spirit because you did it in 'ignorance', so I offer you today atonement even for that sin through Christ.'
Third, for sins where capital punishment was the penalty but not necessarily implying a 'high handed' full rebellion from the covenant, the New Testament provides an atoning sacrifice in Christ, including murder, adultery, etc. Therefore being put to death for sin in the Old Testament is not to imply that each offender could not be forgiven by faith, just not forgiven by Mosaic Law.