I built a service called Invoiced (http://invoiced.com) that has Stripe baked in from the beginning. Your customers pay through a secure form we generate and the receipt is generated/e-mailed to them afterwards.
If you want any more info, you can reach me at jared [at] invoiced.com.
EDIT: Should also mention you can make invoices without making an account at http://invoice-generator.com if you just invoice occasionally.
I use freshbooks [0] and it is awesome. They also have integration options with stripe [1] even though I personally have not used it yet.
Same as above, what if you need to send the invoice after getting paid, not before?
Xero is great. It integrates well with stripe. They're also a full-featured accounting app (more so than Freshbooks which is only invoicing and expense tracking, and they charge as much as Xero).
What if you need to send the invoice after getting paid, not before?
You could still do that. You can create an invoice and apply a credit. They offer a free trial so you can see.
I use the app that I built for this purpose (http://duetapp.com). It has stripe and paypal built in. Customers can download a pdf copy of the paid invoice for their records.