How can such integration benefit users? What are some things it enables?
OT includes bid/ask markets, allowing for trade between assets. And unlike most exchanges, the voting pools feature makes it impossible for the server to steal the coins.
OT incorporates Chaumian blinding (untraceable cash), meaning it can provide anonymity and untraceability, similar to what the Bitcoin community strives for with existing mix services. (Bitcoin by itself is publicly-audit-able, which is a strength, but is also the opposite of untraceable. Its benefit is censorship-resistance, not untraceability, which can be added separately using OT.)
OT has instant finality of settlement (instead of waiting 10 minutes to an hour for a transaction to clear.) This can be useful where merchants and and shopping carts are involved.
Micro-transactions will be more feasible on transaction servers than they would be on the blockchain.
Cash streaming protocols
Cash streaming protocols, in general, should become more prevalent and help to solve issues of resource allocation on mesh networks, anonymous networks, etc. Virtual Tahoe LAFS hosting and so on will eventually become more available, whether via OT or some similar system. (This would help protect the lives of Syrian bloggers murdered by snipers, and the lives of Chinese bloggers unjustly imprisoned to decades+ of hard labor--and to protect the anonymity of Mexicans who otherwise risk being disemboweled and strung from a bridge when following a "Real Names" policy.)
Operates securely on low-trust servers
OT cannot lie on your receipt. It cannot change your balance or forge any of your transactions. (Bitcoin also is like this, but it's still worth mentioning.) Combined with an auditing protocol, this makes it possible to run low-trust servers.
No transaction history
On OT, unlike most other systems, and unlike the blockchain, you will be able to prove which instruments are valid, and which transactions are cleared, without storing any transaction history, as long as you keep your last signed receipt. This is useful to all parties, and also reduces the cost of running a transaction server.
Full range of financial instruments
OT supports a full gamut of financial instruments, including cheques, transfers, cash, cashier's cheques, receipts, recurring payments, market offers and trades, and smart contracts (scriptable clauses - write your own.) You will have to decide for yourself how to best use these capabilities.
You could use OT to write a market exchange, or online wallet or personal wallet. (Of course these exist already, but I'm just saying...)
OT makes it possible to create custom-scripted agreements between parties, to be executed on the server side.
You could use OT to offer escrow services. You could devise your own escrow contract in script form, and then OT will process it.
OT also supports client-side scripting, meaning that people can combine "Unix scripting" with "financial transactions". The possibilities are endless, but that part is really up to the developer community.
You could use OT to build a digital ticketing system, printing out tickets with QR codes or whatever.
In-game representations of real-world financial environments
You could use OT to build a full financial transaction system into an online game or virtual universe. (Gold duplication can get to be a real issue on games.) People on the game would be able to open accounts, withdraw and deposit cash, write cheques, trade on markets, just like people in real life. People would even be able to issue their own currencies, and trade in basket currencies.
Protection against online wallet fraud
At some point OT will support Bitcoin voting pools, meaning it would be impossible for any single server to just disappear with your Bitcoins. (A problem currently endemic to the Bitcoin world.) This will be a protocol between OT servers based on existing features in the Bitcoin script language (like multi-sign.)
This capability goes beyond mere auditing or proof-of-reserves, since it actually prevents a server--or a malicious employee, or a hacker--from stealing the coins.
Open Transactions can benefit bitcoin but there are trade-offs that rarely get discussed. For example, if Open Transactions provides the anonymous transactions and issuing mint functionality for 'tokenizing' bitcoin private keys, it would be a way for the off-line trusted issuers bitbills.com, printcoins.com, and casascius.com to extend their trusted negotiable products back on to the public Internet without accessing the block chain.
After all, those off-line trusted bitcoin products are 100% anonymous and untraceable just like physical cash but they cannot be put online. I could probably accomplish the same thing by sending a certain-denomination bitcoin private key to a recipient over PGP (or Hushmail), but my signing brand would not be trusted immediately. Open Transactions has an open source way to encapsulate anonymously the details of any transaction/contract/etc. In combining it with bitcoin, you definitely add the full anonymity and untraceability, but the bitbills, printcoins, and casascius people would still have to be trusted (and the mint would have to survive).