If you've forgotten an old email address then, unless your memory suddenly improves, the only way you'll be able to find it is by one of the following means:
(a) ask someone who would have known that address if they can remember it, if they've got it written down somewhere or if they've still got emails from you (using that old address) in their inbox ; or
(b) view your profile on a website where you used the old address to register but which doesn't require you to use it to log in now. (e.g. if you used the old address to register on AB, you can click on 'View your profile' and then on 'Edit my profile' to see the address you used here).
The foregoing assumes that you only ever log into your email via the provider's website. If you use a dedicated email client, either on your computer or on your mobile phone, and you've still got mail from the old address stored in that program/app, you can go to an old email and view the address that it was sent to. (If it's not immediately shown, you might need to click/tap on something like 'View headers' or 'Show details' to see it).
If you can find out what your old email address was, you'll only be able to view mail that's been sent to it since you changed addresses if
(a) the provider still exists ; and
(b) they've not disabled your account ; and
(c) you can remember the password associated with it.
Some email providers no longer exist. (e.g. I, and several other AB members, used to use Gawab.com for our email but they've now closed down, so there's no way that we can see any mail sent to our old addresses).
Some email providers don't place time limits on how long an account can remain inactive before they delete it altogether but many (most?) do, so your account might have been wiped from the system. Where an email account is linked to an ISP, and you then change ISPs, some ISPs allow you to continue accessing the account indefinitely but many (most?) block access after a fairly short period.
Unless you can remember your password for the account, the only chance of getting hold of it is if you received mail from that account via a dedicated email client (either on a computer or on a phone). You might then be able to go into the account settings to view the password. (Some such programs 'asterisk out' passwords though, so you might need specialist software to unblock it from view).
IF you can remember/find your old email address
AND you can remember/find the password for it
AND the provider is still in business
AND your account hasn't been deleted through inactivity (or because you no longer use the ISP linked to the account)
you should then be able to go to the provider's website, log into your old account via webmail and view any mail that's been sent to the account since you last used it.