If you're an old veteran at the series, or have bought the game guide, these tips probably won't be anything spectacular. For newbies at the series (like me), these are a couple of tips that might help you out in the long run.
I play the PC version - from everything I've seen the X-box 360 and PC versions are identical, but figured I'd mention that just in case...
Good stat boosts - The amount a stat goes up if you choose to increase it when you level is decided by the number of skill advances in your skills you've had that are tied to that stat. I.E. - get a lot of blade increases, you'll have a bigger gain to your strength stat the next time you level. The skills do NOT have to be your 7 primary skills. So, just as an example , if you wanted to get your Willpower stat up because you're not regaining manna fast enough, you could buy a low-level Alteration spell (since Alteration is tied to Willpower) and cast that spell over and over. If you've got a low Alteration skill (because it's not one of your primary skills), you'll level that skill very quickly (and it won't affect whether or not you advance a character level) and the next time you do level up you'll have a larger increase to Willpower. Destruction spells must be cast at an enemy to level, so that's a bad one to try and 'spam' for a stat boost.
Easy gold - doing the mage guild quests to try and get into the University can be tedious, but it's very much worth doing (especially if you're a caster class). Along the way, you've got to visit every Mage Guild in Cyrodiil. With the exception of one of the guilds, you can loot anything within the guild to then go and sell for extra gold (handy, since you'll be wanting to buy some of the expensive spells in these places unless you're a totally non-magic character). The best loot I've found so far are the 4 pieces of alchemy gear that you'll find scattered all over the place. They have a market value of 50-100 gold each, so just go around until you're encumbered, sell, rinse and repeat. Often you can even sell them in the same guild you stole them from. Just make sure your hand icon isn't red and you're in the clear...
Just because a skill isn't one of your main 7 doesn't mean you can't use it. A lot of the magic schools have low-level spells that are very handy to have (summon skeleton, a low-level conjuration spell, is great to have the first couple of levels; everyone starts with the minor heal spell; and you'll really get tired of having to use a torch all the time, so unless you're playing a kitty you'll want some kind of light spell eventually). Take advantage of the fact that you can learn any skill, Apprentice level isn't that hard to get to with a little practice...
Poisons can be applied to your weapon for a one-shot dose. Applying it to your bow makes your next shot poisoned. Just select the poison like you'd select a beneficial potion.
Power Leveling can be deadly. If you raise your level too quickly, without the loot to buy the good spells/equipment that reflects your level, you might find yourself getting outclassed by your opponents (as a lot of the enemies you face will scale with your level, and they don't have to pay for better stuff it seems).
Okay, those are my random notes for now. Any others out there want to share some good tips with the rest of us?
Kev