I was reading Shivchei HaBesht and came across this quote, which I found very powerful. If you have ever been depressed and wondered whether G-d wants your prayers when you feel like a sinner and worthless - this may help:
ושמעתי מפי ר׳ מנדל מבאר שאמר בימי נעורי בעת חתלחבות בשעת
התפלה עלה במחשבתי איך מלא לבי לחתפלל לפני חשי״ת מוכלל
מפשעים ושבר לבי בקרבי. והיה כך זמן רב ולא יכולתי להפטר ממהשבה
זו כי נדמה לי שהיא מהשבה טובה. ואה״כ השבתי בלבי למה לא נופלת
מהשבה זו במותי ובלבי כשאשב לאכול אצל חקערד. אז דחיתי מחשבה זו:
"I heard from Rav Mendel of Ber who said that when he was young, while praying intensely he would think 'How can I be so bold as to pray before G-d when I am a sinner?' My heart would break within me. This bothered me for a long time and I couldn't get rid of this thought, and it seemed to me that it was a good thought. Afterwards I realised that I only have this thought during prayer, and never when I sit down to eat. Then I was able to get rid of this thought."
In other words, why do we only feel inadequate when we pray? G-d wants our prayers, regardless of who we are and what we have done. If we really felt inadequate we would also be bothered at other times, and not only when praying.
And I felt better! Even if I am not worthy, G-d still loves me!