Answering the question, "Does God work providentially today?" requires a proper understanding of the term and a clear understanding of Scripture.

How does one define "providence"? Dictionary.com says "providence" refers to "(1) the foreseeing care and guidance of God or nature over the creatures of the earth; (2) God, especially when conceived as omnisciently directing the universe and the affairs of humankind with wise benevolence; (3) a manifestation of divine care or direction; (4) provident or prudent management of resources; prudence; (5) foresight; provident care."

The Greek word pronoia, occurring twice in the New Testament, refers to foresight or forethought, i.e., "thoughtful planning to meet a need" [BDAG]. When Paul was tried before Felix, the prosecuting attorney, Tertullus, began his speech by praising the governor: "Since we have through you attained much peace, and since by your providence reforms are being carried out for this nation, we acknowledge this in every way and everywhere, most excellent Felix, with all thankfulness" (Acts 24:2-3). Note its usage in Romans 13:13-14, which reads, "Let us behave properly as in the day, not in carousing and drunkenness, not in sexual promiscuity and sensuality, not in strife and jealousy. But put on the Lord Jesus Christ, and make no provision for the flesh in regard to its lusts." Stated positively, Felix was praised/flattered for his beneficent oversight of the Jewish people; stated negatively, we must not deliberately purpose to fulfill the lust of the flesh. Men can act with forethought, either for good or ill. In contrast, God's providential forethought is always for good, in furtherance of truth and right.

Does God work providentially today? Let us answer this question by asking several other related questions:

Does God answer prayer today? Teaching the disciples to pray, Jesus emphasized things important to God (praise, purpose, proper response) and significant needs of men (provision, pardon, and prevailing over temptation) (Matt. 6; Luke 11:1-3). Other objects of prayer are enjoined in Scripture: We should pray for kings and all who are in authority, so that we may lead a tranquil and quiet life in all godliness and dignity (1 Tim. 2:2). We should pray for those who are sick, that they might be restored (James 5:14). We should pray for the spiritual growth and maturity of fellow-Christians (Col. 1:9-10).

Does God still rule in the kingdoms of men? Indeed. The Book of Daniel repeatedly affirms that God reigns in the kingdoms of men, giving power to whomever He chooses, raising up and casting down (Dan. 2:21; 4:17, 26, 32; 5:18-21). Presenting his sermon on Mars Hill, the inspired apostle said, "He made from one man every nation of mankind to live on all the face of the earth, having determined their appointed times and the boundaries of their habitation, that they would seek God, if perhaps they might grope for Him and find Him, though He is not far from each one of us" (Acts 17:26-27). By urging disciples to pray for kings and all who are in authority, so that we may lead tranquil lives in all godliness and dignity, Paul affirms the continuing validity of this principle (1 Tim. 2:1-2). Has this reality changed? Has God's power and authority diminished? Of course not.

Does God still have a purpose for mankind? Certainly. Ephesians 3:10 speaks of the eternal purpose which He carried out in Christ Jesus our Lord. We are called according to His own purpose and grace which was granted us in Christ Jesus (2 Tim. 1:9). Will He preserve the church of Christ? When Peter made the good confession, "You are the Christ, the Son of the Living God," Jesus answered "Upon this rock I will build My church; and the gates of Hades will not overpower it" (Matt. 16:18). Believers have received a kingdom that cannot be shaken (Heb. 12:28).
Does God still provide for His people? Yes. The Psalmist said, "I have been young and now I am old, yet I have not seen the righteous forsaken or his descendants begging bread" (Psa. 37:25)

In the Sermon on the Mount, Jesus affirms that God will provide food, clothing, and shelter to those who faithfully serve Him (Matt. 6:24-33). Do faithful disciples today enjoy this same assurance? Of course!

Does God still protect His own? Absolutely. No malicious foe can snatch us from the Father's hand (John 10:27-30); no malignant power can separate us from the love of Christ (Rom. 8:33-39). No temptation has overtaken us but such as is common to man; and God is faithful, who will not allow us to be tempted beyond what we are able, but with the temptation will provide the way of escape also, so that we will be able to endure it (1 Cor. 10:13). Again, the apostle said, "The Lord is faithful, and He will strengthen and protect you from the evil one" (2 Thess. 3:3).
Does God still remember His promises? Without doubt. Providence is clearly implied in the many "I will…" passages of promise. Consider God's threefold promise to Abraham of land, nation, and Seed (Gen. 12:1-3, 7). Note His assurance of deliverance from Egyptian captivity (Gen. 15:12-16). Reflect upon His oaths relating to the restoration of Israel (Isa. 44:26; Jer. 7:19; 16:14-15; 30:1-3; Amos 9:11). Consider His commitment regarding the Messiah/Christ (Deut. 18:18; 2 Sam. 7:12; Jer. 23:5).

Conclusion
God still answers prayer today. He still rules in the kingdoms of men. He still has a purpose for mankind. He still provide for and protects His own. He still remembers His promises. Therefore, we assuredly believe that God works providentially today.
Yet, we must recognize the relationship between divine providence and personal responsibility. God provided a ram to sacrifice in the place of Isaac after Abraham demonstrated willing obedience (Gen. 22:1-14). God provided for the physical needs of Israel when they walked in His statues and kept His judgments (Lev. 26:3-10). God delivered Esther and the Jews as she courageously brought the report of Haman's plot before King Ahasuerus (Esth. 4:1-16). God will provide us with the physical necessities of life, but we must seek first His kingdom and His righteousness (Matt. 6:24-33). He has blessed us with the spiritual necessities of life, but we must diligently study and apply His word (2 Pet. 1:2-3). He will deliver us from temptation, but we must diligently look for that way of escape (1 Cor. 10:13).