ALPHA cards are black bordered and have very very rounded edges (2mm radius) compared to all other kinds of magic cards (1mm radius). Just pick up a black bordered card and overlay them on top of each other. If the corners are VERY different then you have ALPHA, otherwise you have BETA.

There are several cards that were corrected between alpha and beta and can be used to instantly identify extremely worn cards. As cited on Wikipedia ^[1]

• Circle of Protection: Black was accidentally omitted from Alpha.
• Cyclopean Tomb had no casting cost, instead of a casting cost of 4.
• Death Ward incorrectly credited Dan Frazier as the artist rather than Mark Poole.
• Elvish Archers had its power/toughness listed as 1/2 rather than 2/1.
• Force of Nature was printed with the letter G in its text box rather than the green mana symbol, and the artist's name was spelled incorrectly.
• Orcish Artillery had a casting cost of 1R rather than 1RR.
• Orcish Oriflamme had a casting cost of 1R rather than 3R.
• Phantasmal Forces was printed with the letter U in its text box rather than the blue mana symbol.
• Red Elemental Blast was printed as an instant rather than an interrupt, making half of its ability unplayable under the rules of the time.
• Sedge Troll incorrectly credited Jeff A. Menges as the artist rather than Dan Frazier.
• Volcanic Island was accidentally omitted from Alpha.

One set that recently came to my attention that is not identified on the identification chart for English cards (see below) is called "Alternate 4th Edition". More info about those cards can be found at The Magic Librarities ^[2], here are the main points:

1. This set is only available in starter decks. Their ISBN is 1-880992-26-4 instead of 1-880992-25-6.
2. The back of the Alternate Fourth Edition cards feel glossy, very much different from normal Magic Cards.
3. Alternate Fourth Edition cards do not glow under ultraviolet light ^[3], while normal cards do.
4. Alternate Fourth Edition cards have a darker blue colour at the top of the letter A from the word MAGIC while normal cards have a light blue colour.
5. The printing pattern is very different. Regular cards have a hexagon pattern, while Alternate 4th Edition cards have an indiscernible pattern.

This Magic Set Identifier flowchart ^[4] will help you determine the set of English cards up to about 2001, beyond there it's fairly easy to identify from the set symbol on the card. Thanks to Hackworth for providing an up to date url for it!

There is an updated version ^[5] of that flowchart that includes foreign language cards as well. While identifying English cards is relatively easy, there are some difficulties with other languages, especially with German Revised White Border Cards (aka "Unlimitierte Edition" (unlimited edition) - not to be confused with the Unlimited set!). Some of them are almost undistinguishable from Fourth Edition cards.

The Green Disenchant Project ^[6] has some more in-depth information and scans that may help identify such cards.

[1] https://en.wikipedia.org/wiki/Alpha_%28Magic:_The_Gathering%29#Errors
[2] https://www.magiclibrarities.net/721-rarities-alternate-fourth-edition-cards-english-cards-index.html
[3] https://www.magiclibrarities.net/721-rarities-alternate-fourth-edition-cards-english-cards-images-light.html
[4] https://i.sstatic.net/Dqc2B.gif
[5] https://i.sstatic.net/rZQcr.jpg
[6] https://greendisenchantproject.jimdo.com/fwb-4th/