Yeah, you have to delete the certificate, which means your computer will give you a warning every time you play.

The minecraft wiki has more info if you need it, look up "mods".
If your computer is warning you I'm pretty sure you're doing it wrong.
I have modded it before, nothing like that happens.
And you can play online with a modded minecraft.jar file; basically everything is handled on the server end.
-Canama
I've never tried mods, because of this article:
http://www.minecraftwiki.net/wiki/META-INF"This directory is notable because it must be deleted to use mods. The META-INF folder contains a digital certificate (MOJANG_C.SF and MOJANG_C.DSA) that contains a checksum of all the Java files. The certificate is issued to prove the code is safe, and is what lets the web applet version of Minecraft run without Java safety dialogs. When the files are modified, they could have been tampered with, and the certificate is invalid (the checksum changes). If a .jar file contains an invalid certificate, it won't run. Removing META_INF removes the certificate, so it will run again, but if you try to use the browser version of Minecraft, you might get warning dialogs. The MANIFEST.MF file is unrelated, and simply contains information about the archive."
That only applies to the browser version, and I can't fathom why you'd use it anyways.
-Canama