When I was starting to become observant, at the end of shacharis one day, someone asked me "are you finished with tehillim?". I told them I don't know what that is. They told me "if we knew what was happening in heaven while we are saying tehillim, we would be saying them all day non stop".
So, a few years later, I still would like to know what the power of tehillim is. What corrective action are we taking by saying them?
At one point as a young student I was informed that a neighbor's wife had become seriously ill, and I began reciting a very lengthy regimen of Tehillim for her every morning after Shaharith, including sections of 119 spelling her name. This made me very late for Shi'ur on a frequent basis, and my Rav finally asked me why I was so late so often. When I told him why, he suggested that it would be better to interrupt my Tehillim to come to Shi'ur on time, because the source we have for the power of Tehillim is a Midrash that says that David HaMelech asked HaShem to receive Tehillim the way He receives Talmud Torah (ie., to make the recitation of Tehillim as powerful as Talmud Torah). The Midrash does not tell us whether or how HaShem responded. Hence, Talmud Torah is at least as powerful as Tehillim. Not to say Tehillim isn't powerful or important, just putting it in perspective. Talmud Torah KeNeged Kulam.
"If you only knew the power that lies in the verses of Tehillim and their effects in the celestial heights, you would recite them all the time. Know that the chapters of Tehillim break through all barriers and soar aloft from level to level unimpeded. They intercede before the Master of the Universe and secure their effect with kindess and mercy."
The summary is as follows. The Tzemach Tzedek saw in a vision a very harsh decree against the Jewish people, especially the Torah community. Nothing could overturn in. The Tzemach Tzedek told his oldest son to get a minyan to say the entire book of Tehillim no later than 4am. For 53 days the minyan took place and then the Tzemach Tzedek had a vision of his grandfather the Alter Rebbe holding 53 books of tehillim smiling.
It is well known that Dawid HaMelekh was the soul of all Israel, as written "The praise of Hashem shall my mouth speak and all
flesh shall bless His Holy Name." The reason it says the words "all
flesh" is meaning at any time (Yismah Yisrael, Parashat Eqeb). Meaning
whenever one is in need, he should pray Tehilim. The Semah Sedeq once
said that if we knew the strength of the Tehilim, and the Heavens we
would recite it every moment.Their actions make kindness and mercy
(ibid.). The Emeq HaMelekh writes (pg. 15) that the book of Tehilim
declines many stumbling blocks and some damages from him and his
household members, and his family as well. It makes great blessings
goodness and merits to him. It is also interesting that the Magen
U'Shemesh writes that Gimatria of the one hundred and fifty Pesuqim is
corresponding to the Gimatria of Pidion (redemption).
The Midrash in Pinhas writes that whatever a person needs, he should recite Tehilim for it. (He should recite it consecutively) and
not stop for the Yehi Rason between the books of Tehilim, until he has
completed the entire Sefer. Through the Tehilim we bring closer the
redemption (Midrash Tehilim, Shir HaShirim). "Whoever recites Tehilim
every day, it is as if we fulfilled the entire Torah (Rabenu Efraim,
Parashat WeZot HaBerakha)." One who wants to have a connection with
Hashem, should recite Tehilim (Shala, Nazir 257). The Noam Elimelekh
writes that Tehilim have the possibility to make drastic changes and
there is no Sat-an or obstacle stopping them. The Shebut Ya'aqob
writes (Heleq Bet, Yoreh De'ah 44) that if one desires to make many
prayers, he should recite Tehilim, because it is leaning Torah, and
there are many good omens in it. Rabbi Haim Palagi writes (Minhagi
HaHabi"f 80) that one who recites Tehilim (and Brikat HaMazon) daily
lengthen their years and days. Rabbi Haim Palagi also writes that this
worlds stands upon Tehilim, and one redeems themselves from any
damages and redemption will come through the recitation of Tehilim
(Haqdama, Kol HaKatub LeHaim). One who recites Tehilim daily merits to
be under the Kise HaKabod (Chair of Honor). We have nothing greater
than Tehilim because contains everything (Shala).
There are countless compliments and praises of the sacred and holy book of Tehilim, and one could go on and on upon its' praise, so
always remember, we can save many people from sickness or anything bad
by just reciting Tehilim!
The Baal Shem Tov stated that if Psalm 119 is said every day, a person will be able to enter into a meditative state when talking to another and receive deep perceptions about that person. ("Rabbi Nachman's Tikun Haklali" by Daniel A. Elias.)
The 3rd Lubavitcher Rebbe, known as the Tzemach Tzedek said in the name of Rabbi Yehuda "Whatever Dovid Hamelech say’s [sic] in his book pertains to himself, to all of Israel and to all times.”
“If one would only know the power of verses in Tehillim, and their effect on high, one would recite them continually. The verse of Tehillim transcend all barriers and ascend higher and higher, imploring the Master of the Universe, until they achieve results of kindness and mercy.” (Hayom Yom)
• Maharsha says that Tehillim brings one to fear of Hashem.
• Peleh Yoetz says, “One who routinely says Tehillim is protected from all harm befalling his house, his family etc. One who wishes to attach himself to Hashem and His praises should be connected to sefer Tehillim. We have a tradition that one who has a problem, or pain, or is going on the road, should read the entire Tehillim all day without stopping, with kavana and humbleness. He will see wonders. is tradition has been tried and tested (and works)."
• Tehillim protects you in this world and in the next.
• One who says Tehilim for forty days is saved from harmful events.