The bible was written in a time of a primarily oral culture. Repetition is often used for emphasis or to drive home a point (as Seeker of Truth mentioned), and to make things easier to remember. So important things were repeated a whole bunch of times in slightly different words to make it easier to remember. Even if you didn't remember it the first several ways they said it, if you hear the same message over and over it will sink in.
However, in some of these passages you point out, the repetitiveness is more an artifact of these books presenting a historical record, in a detailed and factual way. That passage from Numbers 7 almost reads more like a transaction register...there are multiple ways to account for this.
One, building the tabernacle, a home for God on earth, was a really big deal...so important that they were quite meticulous in documenting what God's instructions were about building it, and how Isreal did on their quest to implement God's directions (and of course, it's just about always significant when there's a deviation from the usual pattern or someone didn't follow through correctly. So what we're seeing here is every tribe followed through and sacrificed all the required sacrifices as required, along with details about who did what when.
Secondly, it reads more wordy in English in general, because in many cases a hebrew word becomes an entire phrase in English because we don't have a consise word to accurately describe the same concept. Not to mention, Hebrew uses a lot of prefixes instead of joining words (so "and" and "for" and so on are not seperate words) so there's less words overall. So if you spoke Hebrew, and read the same passage in Hebrew it would be shorter and sound a lot less redundant. A typical example phrase from Numbers 7, "And for a sacrifice of peace offerings" instead of being 7 words becomes only 2 words in Hebrew (וּלְזֶבַח הַשְּׁלָמִים, or transliterated, ûl'zevach haSH'lämiym).
Third, in some cases, it's hard to read because of the formatting chosen by the particular bible pulisher. Much of Numbers 7 looks like tabular data. If it were lined up into nice neat columns where "5 male goats" lines up neatly for each of the 12 tribes it would be much quicker and easier to realize the words are the same for each tribe, than when each tribe's sacrifice is presented as a multi-line paragraph.
As far as Leviticus 13-16, this portion is pretty much a medical manual for the priests. You might compare it to sitting down and reading the physician's desk reference today. It's going to be very detailed, because it's about how to diagnose whether a particular skin disease is of a leperous nature or not. Lepers had to be isolated from society, so it was a very serious condition, and differentiating harmless conditions from serious ones is kind of important, ya know? So they take their time in being very detailed in describing similar ailments and what symptoms are or are not indicative of leprosy, and how to disinfect the home of a leper and atone for their sin and so forth. Kind of one of those things that's not super-exciting in our day to day life where it doesn't seem very relevant, but if you had someone around you with a contagious skin disease, you'd probably suddenly want to read in detail to avoid it spreading to you ;-).
Additionally, you didn't specifically mention this in your question, but I imagine you noticed significant parts of Exodus and Leviticus are repeated very closely in Deuteronomy. That specific mass repetition is in large part because the end of Exodus and Leviticus were a historical record of Isreal right after they left Egypt. But then as we learn about in Numbers, they weren't obedient to God and spent 40 years wandering the desert, until almost all of the previous generation had died of. So Deuteronomy is in large part Moses's "final speech" to this new generation of Isrealites just before the enter the promised land, as most of them hadn't been born when this important message from God was delivered the first time.