We have CONCUR, linked with corporate purchasing cards, which in our case happens to be MasterCard.
After getting over the initial hump, I love the system. Things we charge on the corporate card are automatically linked in, and anything else I need reimbursed I can just enter manually. The ability to upload documentation - either scanned images or e-mail receipts is great.
I like the ability to begin an expense report as soon as a trip is known and to then add expenses to it as the occur over time before finalizing it when the trip is concluded.
There are wacky times where I just have to fudge something, like tax added to a hotel bill that doesn't penny balance when you break it out over the multi-day stay, but there is a way to adjust one of the days so you do balance. The system - at least our application - only has 3-4 boxes for hotel fees, so in a rare case where there are more taxes than lines (county, city, convention, etc.) I can just add a couple of them together and attach a note.
Not specifically CONCUR, but my company ties the reimbursement process to the payroll feed, so the next time the push out payroll I'll also get the reimbursement. Similarly, any money I owe them (non-reimbursable expenses from the corporate card) just get taken out of my next "check".
Some bills come through very clearly - airfare charges for one, others, like hotel bills take a bit of work.
The system also allows for proxies, so people with assistants can have them enter and reconcile the expenses for them.
We also have the ability to charge travel directly to our account line, avoiding the credit card completely, but only if we use the company travel agency, which I won't do since they're terrible.