Clearly, yes! Consider the following passages from just our reading today:

Then David spoke to the chiefs of the Levites to appoint their relatives the singers, with instruments of music, harps, lyres, loud-sounding cymbals, to raise sounds of joy. So the Levites appointed Heman the son of Joel, and from his relatives, Asaph the son of Berechiah; and from the sons of Merari their relatives, Ethan the son of Kushaiah, and with them their relatives of the second rank, Zechariah, Ben, Jaaziel, Shemiramoth, Jehiel, Unni, Eliab, Benaiah, Maaseiah, Mattithiah, Eliphelehu, Mikneiah, Obed-edom and Jeiel, the gatekeepers. So the singers, Heman, Asaph and Ethan were appointed to sound aloud cymbals of bronze; and Zechariah, Aziel, Shemiramoth, Jehiel, Unni, Eliab, Maaseiah and Benaiah, with harps tuned to alamoth; and Mattithiah, Eliphelehu, Mikneiah, Obed-edom, Jeiel and Azaziah, to lead with lyres tuned to the sheminith. Chenaniah, chief of the Levites, was in charge of the singing; he gave instruction in singing because he was skillful. Berechiah and Elkanah were gatekeepers for the ark. Shebaniah, Joshaphat, Nethanel, Amasai, Zechariah, Benaiah and Eliezer, the priests, blew the trumpets before the ark of God. Obed-edom and Jehiah also were gatekeepers for the ark... Thus all Israel brought up the ark of the covenant of the Lord with shouting, and with sound of the horn, with trumpets, with loud-sounding cymbals, with harps and lyres (1 Chronicles 15:1-24,28).

He appointed some of the Levites as ministers before the ark of the Lord, even to celebrate and to thank and praise the Lord God of Israel: Asaph the chief, and second to him Zechariah, then Jeiel, Shemiramoth, Jehiel, Mattithiah, Eliab, Benaiah, Obed-edom and Jeiel, with musical instruments, harps, lyres; also Asaph played loud-sounding cymbals, and Benaiah and Jahaziel the priests blew trumpets continually before the ark of the covenant of God (1 Chronicles 16:4-6).

What is more, many of the psalms of David have in their superscription that the psalms were to be sung with instrumental accompaniment. 

For the choir director; with stringed instruments, upon an eight-string lyre. A Psalm of David (Psalm 6).

For the choir director; upon an eight-stringed lyre. A Psalm of David (Psalm 12).

Even within the psalms, the accompaniment of musical instruments in praising God is encouraged:

Give thanks to the Lord with the lyre; Sing praises to Him with a harp of ten strings. Sing to Him a new song; Play skillfully with a shout of joy.(Psalm 33:2-3).

Sing for joy to God our strength; Shout joyfully to the God of Jacob. Raise a song, strike the timbrel, The sweet sounding lyre with the harp. Blow the trumpet at the new moon, At the full moon, on our feast day (Psalm 81:1-3).

To some of you this is a non-issue. You never imagined that anyone might judge you for worshipping God with a musical instrument. But there is such a group that would do just that. They are a good-sized denomination within the Christian faith calling themselves "the Church of Christ". While I do not contest their preaching of the Gospel, I would take them to task about their overly judgmental attitude regarding the use of instruments in worship. Although they try to defend their position from the Bible, the arguments that I've read from them seem to me a mishandling of Scripture, such that they fall into the error of proof-texting, namely, making an argument from silence (e.g. the New Testament does not directly mention instruments in worship except in the Book of Revelation) and then using the Bible to prove their point regardless of context and the proper use of hermeneutical rules for interpretation.

While anyone is free to use or not use musical instruments when they sing praise to God, I believe the Bible permits, models and even encourages it. The above Scriptures are simply a snippet of what the Bible says about the use of musical instruments in worship in the Old Testament. Now, the New Testament does not have a lot of Scriptures that speak about the practice of worship in general, but when the New Testament encourages believers to "sing psalms, hymns and spiritual songs, singing and making melody with your heart to the Lord" (Ephesians 5:19), I believe Paul had the psalms of David in mind, which were often accompanied by musical instruments.