It depends on how far you've gone in the deletion process and which e-mail programs & providers you use. There is generally a "Deleted" folder you can click on in every e-mail program, and in some cases items emptied from that folder can be found in your Recycle Bin. With internet e-mail accounts they will usually permanently delete that information within a set time-frame, however. If the e-mails you're searching for are there, in most programs you simply have to drag them back to your Inbox, or another folder you've chosen. For Hotmail you check the box beside the deleted e-mail and select the drop down menu called "Move to" and pick the place you want it to go to.
Without using specialty software for recovering deleted information (such as the forensic programs used by law enforcement) you have a few other options available to you:
1) You can do a system restore on your computer if you know exactly when those e-mails were still available, although that doesn't always restore e-mails - it's something that depends on how it was originally set up to store the information on your hard drive for restoration purposes.
2) You can check your "Sent" folder (which most people forget is even there) and if you've responded to those e-mails, the deleted e-mail will likely be part of your response (it depends on your settings, though).
3) You can check on the server where your e-mails are originally stored. Different types of e-mail accounts are stored differently. Some are backed up automatically on a server (usually a company you work for will have this feature in their e-mail system, or they'll have back-up tapes that can be loaded, assuming your messages are important enough for them to take the time to restore them). Some e-mails are automatically deleted from the server when they're downloaded to your computer, and some are kept on the main system. You won't have any control over something like a Hotmail or Yahoo! account, but if you use the e-mail you've set up with your ISP (internet service provider) you may have all kinds of control, back-ups and storage you're unaware of.
4) You can also have your friends & colleagues re-send their e-mails to you if you're desperate.
Without knowing exactly what type of account, ISP, program and/or server you're using, there aren't any easy answers, but I hope some of the information I've given you will be of help to you. There are other options, but there is more work involved usually, and they can be difficult to explain (particularly without other specifics).