Must one, should one, or can one pray every little detail of life? For example, can one pray for his sports team to win? Is there a limit of what to pray for?
It's a great idea to pray for everything ever so little it might be.
R. Miller zz"l said, that person should pray for everything to Hashem and thanks Him after the event happened, no matter what the result was. That practice can bring person closer to Hashem (attain for himself emuna and betachon), besides of the other benefits, that that person achieves with his prayers.
Rabbi Nachman from Breslev zz"l said to his student Rabbi Nathan from Nemirov, that a person shouldn't be ashamed to ask Hashem even for a button for his shirt if he misses one.
Similar idea told about Chazon Ish, that when he needed new pair of shoes he stand in the corner and prayed for that.
A little joke about the matter. Rich guy prays to Hashem and says: Dear Hashem please give me health and long life. And please don't worry about my income - I can nicely manage it myself.
For the objection that there are things, that person shouldn't pray for. I heard that even if a thief goes to do his not nice things and prays to Hashem to help him, Hashem listens to him and enjoys his prayers.
I think, once person realizes, what power the prayer has and gets closer to Hashem, he won't spend such a powerful thing on things, that against Hashem's will. For sure he would not do it if he prays, that Hashem guides him in his prayers.
There are many books about prayer for big and little things.
The over one, that I know is "In Forest Fields" by Rav Arush from http://breslev.co.il
While I suspect this may not be what you were looking for, it should be noted that we are not allowed to pray for things that are either false or already exist.
The example given of what's not allowed is if a traveler is returning to his city and hears a far-off cry in the city and prays that it did not come from his house. Because the facts are already established - that is, the cry either did or did not come from his house - and no prayer is going to change the facts, this type of prayer is prohibited.
Moed Katan 18b:
Rava heard a guy davening to marry a specific girl. He told him, don't daven like that - if she is fit for you, you won't lose her, and if she isn't fit for you, you are denying G-d...
At the very least, a person should not daven for a specific shidduch. Some want to extrapolate to all things - at the very least it should be applicable to job and property, as those things are also decreed who will get what. Some things may be, unbeknownst to you, bad for you, and if you daven for them you may get them.
Rav Pam used to say (quoted in Artscroll's biography of Rav Pam) that in the request we make in the Yehi Ratzon before announcing the new moon, the clause אהבת תורה ויראת שמים (that we should have love of Torah and fear of Heaven) was a "more important" request than that of חיים שימלא השם כל משאלות ליבנו לטובה (a life in which all of our requests should be fulfilled) because your requests may not be for the objective best. Sometimes it is better to leave it up to Hashem to know what is best for you.