The various Senator's Endorsement (one for each region) and most of the one-use endorsements by historical figures (Jefferson Davies, James Buchanan, ...) are usually among the first events played; Endorsement: James Buchanan stays strong for more, as it helps tip the balance in contested slave states; finally, the two Governor's Endorsement are treasured towards the end, especially in the last turn, after you lock someone out of his region (or something similar).
If someone is adding cubes to undisputed states they control in a single region, they might be sitting on that region's regional polling card (or they have one of the events that move the polling to a different region) and preparing to lock their states. If you aren't under attack elsewhere, it might be a good idea to add cubes to the states you control in that same region to be able to lock them.
Your personal appearance is very powerful and should be used sparingly; in general, it is most effective in the last turn, when it's harder for your opponents to counterbalance it. The card Speaking Tour allows you to get one more (or one, if you're Lincoln); if you get it, I strongly advise you to use it.
Locking someone to a single region (Coal Shortage) or out of half of the country (Uncle Tom's Cabin Reprinted, Underground Railroad) for a turn can be beneficial and may help forming alliances against runaway leaders (as everyone is free to pick on them with a minimal chance of retaliation).
The Accursed Three. For each of Virginia, Ohio and Indiana there is an event that takes away half of the controller's influence (rounded up) and gives it to who played the event. Those are, respectively, Coal Miners Demand Better Treatment, Radicals in Cincinnati and Railroad Strike. This means that usually these states are among the last to be taken (unless someone has the event in hand), and that the controller tries to keep an even number of cubes there, to minimize damage.
Californian Gambit. If you have the Pacific West regional polling card in the first turn, it's good to get California and lock it, as that will probably make you first in Momentum; your lead will also be a small one, so it shouldn't be hard to slide back to one of the last positions, which are better for the last turn.
Southern Sweep. A good strategy for Breckinridge (sometimes in collaboration with Bell) is to quickly lock the Lower South; there are 7 lockable states there, and they take only 38 cubes (Breckinridge can already have 11 cubes in LS at the beginning of the game); this has the side effect of making South Carolina harder to hold (speeches in LS will only target that state, if the others are all locked), but allows you to concentrate elsewhere for the rest of the game.