ANSWER: Covenants, by definition, are agreements between two or more parties that contain promises to be fulfilled by at least one of the parties. Requirements that are agreed to be met before a promise is fulfilled may also be included, although some agreements can be unconditional. There are many covenants in the Bible!
Some covenants are strictly between individuals and others are between nations. God has made several agreements, both conditional and unconditional, between himself and individuals, or whole nations, or even between himself and all humans! The Bible also contains covenants that are directly not designated as such, like the agreement the Lord made with Adam and Eve concerning what fruit they could eat and not eat in Eden.
Covenants in the Bible were ratified by the "giving of hands" (Ezra 10:19), loosening a shoe (Ruth 4:7 - 11), by written agreement (Jeremiah 32:10 - 12), giving presents (Genesis 21:27), through a meal (Genesis 26:28 - 30), offering a sacrifice (Genesis 15:9 - 17) and other means.
Below is a list of some, but by no means all, Bible covenants.
God made an agreement with Noah to save him and his family (Genesis 6:18). He also made an unconditional promise to him and his descendants that he would never again destroy the world by a flood (Genesis 9:9 - 17). Rainbows are a sign of His promise made to all humans.
An covenant was made with Abram (Abraham) to give him and his descendants the land we call Israel and to destroy its then current inhabitants because of their great sins (Genesis 15:18 - 21).
God made an unconditional covenant with Abram, whereby he changed his name to Abraham and designating him the father of many nations and millions of descendants. Abraham's and his descendants' part of the agreement was to have all their males circumcised (Genesis 17).
Abraham, at the behest of Abimelech, makes an agreement with him to treat him fairly and justly (Genesis 21:22 - 32).
A conditional covenant was made with the children of Israel, requiring their keeping God's law and circumcision, in return for physical blessings. (Exodus 19 - 24). Further terms (conditions) of this agreement were expounded later (Leviticus 25 - 27, Deuteronomy 29 - 31).
An covenant was made with the Israelites regarding the Sabbath (Exodus 31:14 - 18), the commandments and God's Feast days (Exodus 34:10 - 35).
God made an unconditional covenant with King David that there would never lack a person to sit on his throne (Jeremiah 33:19 - 36).
The most important agreement in the Bible, called the New Covenant, was established by Jesus upon His death (Jeremiah 31:31 - 34, Matthew 26:28, Mark 14:24, Luke 22:20, 2Corinthians 3:6, Hebrews 7 - 10). Paul stated that Christians are commanded to commemorate his sacrifice, which made the agreement possible, by yearly taking the symbols of the Christian Passover which are unleavened bread and wine (1Corinthians 11:23 - 25).
The word "testament" is interchangeable with the word "covenants." The King James Version Bible translates the Greek word diatheke as both of these two words. This means we could just as easily refer to the Old and New Testaments as the "Old Agreement" and the "New Agreement."