I dump in clear plastic bags; I don't split the load over two bags, as that would be too messy.
Uh...just kidding.
Sorry, I couldn't resist. Let's start over. I dump at a bank that doesn't charge a fee to take coin in bags. Some banks charge a fee to take coin, such as $3.75 per bag; these are the ones you want to stay away from, if you can. If you must pay a fee, then be sure to dump the maximum amount of coin every single time you go to the bank (and within their acceptable limits per day/week). Rolling is just too much work, especially if you're talking about thousands of coins etc. I have called several banks on the phone to ask them about their policies on returning bagged coins, but many banks will give different answers and different people at the same bank will also give you different answers. Sometimes, you will get a better answer in-person...for example, when talking to a new accounts person at the bank, ask them 'If I open an account here, do you charge customers a fee to return loose coins in bags?" . See what they say. Your mileage may vary (YMMV), but I have found that bankers tend to be more reasonable when they are face-to-face with a potential client (after all, they make money when you deposit your money). This is especially true if it's the lead new accounts manager on duty that day that you're talking to. If they are OK with taking bagged coin, then when you sit down with them to open account, say, "Before I open the account, I just want to know what your limits are on bringing in bagged coins, how much etc" . It's a good idea to know in advance and I also think the honest approach works best (seriously).
Also, don't give up if they won't take coin in bags or if the fee is too high. Then I change course and ask them, "can I order coins as a customer here and if so, do you charge a fee?" If you can't make it a dump bank, see if you can make it a bank where you can order boxes for free.
I don't use Coinstar, as I don't always want to go shopping with the money after returning the coin (ie Coinstar machine at Wal-Mart). Just not worth it in my opinion, plus I hear the machines are a lot slower than the good coin counters at a regular bank (if you have them in your town).
For dumping large amounts of coin (ie > $500) for a normal (non-business) account. Well, I think HoardCopperByTheTon or Market Harmony would be able to answer that question better, since they tend to handle higher amounts than a lot of us here. But in general, the safest thing to do is to split it up over several branches of the same bank and not all in the same business day (FYI: It may take 3 days for the deposit to be posted). For a non-business account, I would think $100-$200 in bagged coin on a regular basis should not be a problem, as long as it's not every day etc. If it's half dollars, I wouldn't go over $500 per dump (again, YMMV; some members here dump a lot more than one box at the same time). The amounts could probably be safely higher if it were a large national bank (ie BofA, Chase, Wells Fargo, National City) in a major metro area. I'm sure others here with more experience can chime in on this subject.