Signs are definitely used in the Old Testament. Generally they are used to confirm that a calling (as with Moses), a command, or a promise (as with Hezekiah) was indeed from God. Specifically, they were used in God's dealings with the Jews and not with the Gentiles. This is seen in biblical practice (Exodus 4:8-9) and in Jewish expectation (1 Corinthians 1:22).
Signs are also used in the New Testament. Specifically, they were used to confirm that the words spoken by the apostles were indeed the words of God. This was needed because there was no such thing as a written New Testament at the time. Miraculous signs proved that their words were from God. The key verse for this is Mark 16:20 - "And they went forth, and preached every where, the Lord working with them, and confirming the word with signs following. Amen." Another point is that New Testament signs were mainly addressed to the lost. Therefore, we are told that "tongues are for a sign, not to them that believe, but to them that believe not" (1 Corinthians 14:22).
As to asking for signs, this is certainly a questionable act in scripture. Christ said to those who sought from Him a sign, "An evil and adulterous generation seeketh after a sign" (Matthew 12:39). Evidently, seeking a sign places one in the camp with those who tempt the Lord. If God's way is made clear in the scriptures, then to seeking a sign is an ultimate act of disbelief.
On the other hand, if the way of God is really not clear, that does not give us the right to ask for a sign. This assumes our right to demand an answer from God. He may choose to keep us in the dark for some time, but that is His choice. To seek a sign is to attempt to force God's response in a way acceptable to us. It is an act of rebellion.
It is best to keep away from seeking or demanding signs from the Lord. Ask patiently for guidance. Sometimes, He may answer in spectacular ways; sometimes, He may guide us in the most subtle of ways. But trust always that He is leading and He will lead.
