There is no standard for posters. The answer really depends on how you plan on printing the posters.
If you will be printing a small quantity (let's say 200 or less) you may want to print digitally. Digital printing is very similar to a color copier or color laser printer. Many places (Kinkos, OfficeMax, Staples, etc.) can do digital printing for you.
If you do choose digital printing, there are two standard large sizes (in the US) 11" x 17" (Tabloid) or 12" x 18".
If you will be printing a larger quantity, or if you need special processes (specific inks, coatings, etc) you will probably choose an offset printer. This means a press.
Once you make the decision to move to a press, the issue of size is solely dependant on the size of the presses your printer has. Most printers will have no problems printing 30" to 40" wide. Since the paper for a press comes on a roll, you can make the other side pretty much as long as you want (with limitations - talk to your printer).
The third option is to use a large-format inkjet printer. This is largely how billboards and banners are made. These printers can print HUGE sizes. You can expect to pay $7 - $30 per square foot for this option depending on b&w vs. color and what material you print on. Places like Kinkos, OfficeMax and Staples usually have 60" large-format inkjets which means you can make your poster a maximum of 5 feet wide by whatever (because the paper is on a roll). You can also find other printers that can print much larger sizes on inkjets - 30 feet wide or more!
To summarize: there are no standard poster sizes. There are a few standard paper sizes for use in digital printing.
I generally offer my clients 11" x 17", 12" x 18", 24" x 36" or 36" x 60".