I once heard from a great Rabbi that the definition of worship is when you consider someone absolutely perfect in every way, and this feeling is despite their flaws, and arises because you think they are perfect, and therefore the 'ways' about them are all perfect too. Whatever the theological issues one is experiencing, if one really loves Hashem with a true love, one will find everything about Him is praiseworthy...
A common misconception about Hashem ית׳ is that a difference between Him and us is that we are limited in our strength and ability, while He has infinite power to do anything. Therefore, we conclude, if we were God, we would also be able to do all that, so what's the big deal.
Firstly, this type of thinking is the opposite of humility. Moshe Rabbeinu was praised for being the most humble man alive, and the Lubavitcher Rebbe explains that this is because he always felt that if any other person on the planet was endowed with his abilities, they would do a better job than him. Nowadays, many people indulge in the opposite. They think if they were a billionaire, or the president/dictator, or the CEO of a big company, or the developer of the product they are using, or a Rabbi, that they would do a much better job than this schmendrick.
Not only that, but it is incorrect. Hashem is not "the same as us except that He is infinite". This theological point is brought in the first Rambam in Mishnah Torah:
יְסוֹד הַיְסוֹדוֹת וְעַמּוּד הַחָכְמוֹת לֵידַע שֶׁיֵּשׁ שָׁם מָצוּי
רִאשׁוֹן. וְהוּא מַמְצִיא כָּל נִמְצָא. וְכָל הַנִּמְצָאִים
מִשָּׁמַיִם וָאָרֶץ וּמַה שֶּׁבֵּינֵיהֶם לֹא נִמְצְאוּ אֶלָּא
The foundation of all foundations and the pillar of wisdom is to know
that there is a Primary Being who brought into being all existence.
All the beings of the heavens, the earth, and what is between them
came into existence only from the Truth of His being.
The truth of His being is what is called a True Being. This is how it is explained. You and I are not a true existence, and the proof is, we have zero say in our existence. We can't create ourselves, and we can't stop ourselves from dying. We came into existence at a certain point, which means we weren't "always there". We are not the masters of our existence and being at all, but He is completely. This is incomprehensible to us, and sounds like a paradox, but clearly this has to be the case, He is absolutely His own master and there is nothing about Him that is dependant, incidental, or in any way not His. As the Ramchal puts it in Derech Hashem:
כי הנה הוא ית״ש שלם בעצמו ולא במקרה
For surely He, may His name be blessed, is perfect from Himself, and
not contingently so.
The Kabbalists describe Hashem's existence as utterly personal to Him. We cannot comprehend any of this. The real question is how are we ever befitting of praise, especially the praise He gives us!
Thus, any greatness we perceive in Hashem is something to praise Him for, absolutely. Even if one wishes to make the argument that we can only perceive Him from a human perspective, that doesn't do the infinite sublime justice He deserves, still this is the rule: whatever we perceive as praiseworthy, Hashem is infinitely more than that, and we should in fact be afraid that whatever praise we offer is not enough. It's a bit of an insult to praise Einstein for knowing that 2 + 2 = 4, and this is why we are told that if it weren't for the Torah, we wouldn't be able to praise Him.
I hope this settles an unaddressed theological misconception, which I believe goes well with ray's answer, as well as mevaqesh's comments on user613's answer, on Hashem's free will.
So what sort of things does the Torah and do Chazal praise Him for? I won't be able to go into a lot of detail and this is best left as a personal journey of discovery, but here are some of the headers.
His creation is mind-blowingly amazing for any mortal being. Firstly, its size - it is big in an absolute sense. There is no finite being that can comprehend both the depth of the plank scale, and at the same time the depth of cosmic scale, and if one were large enough in scale to see the universe as small, time would pass so fast that the universe wouldn't exist. No machine can calculate the number of particles, not to mention stars, and their states and interrelationships with every other particle, yet He suspends, sustains and controls this personally with His will every instant. His laws of physics, and the world of knowledge, and His general wisdom is certainly something any human being would find immensely amazing, and then boundaries of what there is to find out and discovery is endless.
Just because He could supposedly do all this easier than it is for me to lift my elbow, it is still amazing in my eyes, and with the above discussion in mind is a personal fact about His Self, and therefore He is praiseworthy.
יְהַלְלוּ אֶת־שֵׁם ה' כִּי־נִשְׂגָּב שְׁמוֹ לְבַדּוֹ הוֹדוֹ עַל־אֶרֶץ
Let them praise the Name of the Lord: for His Name alone is exalted;
His glory is on the earth and heaven.
A gemara explains that he gave Nevuchadnezzar might, and assisted him in his idolatrous battles and all the related travesties, because He wanted the person who did the necessary evil of destroying the temple to be great, so as not to degrade the Jewish people that they were conquered by a weak army.
The Tanya discusses all of the things Hashem did that He hates doing, bishvil Yisrael. He made a tzimtzum and allowed someone else into His personal and private existence, He hid, He created a yeitzer hara and evil and suffering... the list is painful to read.
He runs the world with hashgacha pratis (see Derech Hashem 2 for full details), ensuring that we have free will, yet our free will doesn't interrupt His plan. He helps us, saves us, rescues us, teaches us, rebukes us, gives each creature food, every person a soul mate (and arranges their meeting)... His deeds are awesome!
Yaacov Avinu A'H praised His deeds and His character in the following statement, which will lead us on to the next point:
קטנתי מכל החסדים ומכל־האמת אשר עשית את־עבדך
I am unworthy of the least of all the mercies, and of all the truth,
which Thou hast shown Thy servant (Bereshit 32:11)
First of all, the fact that He even has a character, so-to-speak, is a surprise and worthy of praise, as nobody tells Him He should have a any preferences. Theological musings make that impossible for us to understand, as surely everything should be completely homogenous to Him, yet when He reveals Himself in the Torah, we see that He likes good and hates bad. If we learn about His preferences we will learn to praise Him, as His so-to-speak personality is absolutely wonderful in every way and absolutely perfect.
We praise His love, His righteousness, His kindness, His mercy, His loyalty and commitment and so much more, just open any random page of Tehillim, or any siddur! Also from our day-to-day experience: He is the perfect parent, infinitely patient with His children, guiding them without infringing on their free will, bringing out the best in them in a dignified way. He remains hidden and, even though He intimately knows the thoughts and feelings of man, stays silent when the wicked curse Him, and holds back when He sees us making mistakes, allowing us to figure it out for ourselves. If we understand that He is perfect, this means He is also perfectly sensitive and vulnerable (in the positive, character-sense, so to speak), yet His Self-control is mighty.
There is a gemara that explains that Hashem's might is that He was able to stand by and watch wicked people do the necessary evil of destroy His temple and His people. A mortal wouldn't have been able to do that.
His being ours
In His great humility, He decided with perfect free will to create us so that He could have us (see second Rashi on Bereshit 1:1), from His own desire (Bamidbar Rabbah 13:6; Midrash Tanchuma Bechukotai 3:1, Nasso 16:1; Tanya 36). Desiring to not be only Him, but have us, is perhaps His greatest praise. He wants and needs us, even though by every right He shouldn't, and becomes ours. For this, we praise Him:
אֵלִי אַתָּה וְאוֹדֶךָּ אֱלֹהַי אֲרוֹמְמֶךָּ
You are my God, my Lord I will praise You (Tehillim 118:28)
We were created to praise Him (Yeshayahu 43:21). Once we move past viewing Him as an "other", as some incomprehensible ultimate force of nature, but get personal and realise He is the Someone of all someones, and we are His and He is ours, then we can praise Him, Himself. Not anything about Him, but just Him. Praising the things about Him, so-to-speak, is something we shouldn't do in excess, because we risk making it sound that it's just the things about Him that impress us. This is akin to a husband telling his wife that he loves her because she is good looking, chas veshalom. This is a hard concept to get our heads around and takes life lessons and maturity, yet it stares at us all the time in the Torah, and in life. Hashem is One, He is not composed of parts, don't attribute a shituf to Him, don't worship His works. We are meant to get in touch with His Essence, as well as the essences of the ones we love in our lives.
[There is so much to draw from, I run the risk of making an already too long post into a full blow dissertation so I'll stop here, although I'll probably add a few more links in future. I hope that I've begun to answer the question and give an example for each person to come to recognise Hashem's greatness in their own way, with the help of His revelation in Torah and ma'amrei Chazal]