Some people feel they are unworthy to daven, but everyone must know that Hashem listens to תפילת כל פה, whoever turns to Him in prayer.
Rebbe Pinchas Koritzer zt'l once said to a Yid who had several children dying young, "My friend, I plead to you: Why do you allow your children to die? Don't you believe that when one davens sincerely to Hashem, even if he is the greatest rasha, he will receive anything he wants from Hashem" (Imrei Pinchas, Toras HaAdam 50)?
The name of this man was Avraham Cohen. Rebbe Pinchas Koritzer understood he wasn't davening sufficiently for his children's health because he didn't think his tefillos would help. Reb Pinchas Koritzer explained that Hashem listens to everyone's tefillos, even the tefillos of the greatest rasha, and Hashem will grant him his requests.
And just as Hashem listens to everyone's tefillos, Hashem will save even the reshaim of the Jewish nation when we daven for them.
The Zohar (vol.1 106.) discusses the differences between the tefillos of Noach, Avraham, and Moshe Rabbeinu. "Who is a compassionate father like Avraham? When Hashem told Noach that he should build a teivah because He was about to destroy the world, Noach was silent. He didn't say anything. He didn't daven. But when Hakadosh Baruch Hu told Avraham about the sins of Sedom and that He is contemplating destroying them, immediately (18:23) ויגש אברהם ויאמר האף תספה צדיק עם רשע, 'Avraham came forward and said, 'Will You also stamp out the righteous along with the wicked? … Reb Alazar says, "Avraham also didn't daven with perfection. Noach didn't daven at all. Avraham davened that there should be justice and that the innocent shouldn't die together with the guilty. But he didn't finish. He didn't request that whether they are worthy or not, Hashem should save them. Who davened correctly? Moshe Rabbeinu.
When Hashem told him (Shemos 32:8) סרו מהר מן הדרך אשר צויתם עשו להם עגל מסכה וישתחוו לו, 'They have strayed quickly from the way that I have commanded them. They have made themselves a molten calf and bowed down to it.' Moshe davened for them immediately, as it states (Shemos 32:11) ויחל משה את פני ה' אלקיו, 'Moshe pleaded before Hashem his G-d…' and he said that if Hashem doesn't forgive them, his name should be erased from the sefer Torah. He didn't stop davening until Hashem said, סלחתי כדבריך, that He will forgive them. But Avraham's prayer was dependent on the tzaddikim, and if there weren’t tzaddikim, he didn't ask that they be saved. So, there wasn't a person who protected his generation like Moshe Rabbeinu, for he was a loyal shepherd."