A significant number in Judaism - the total number of commandments. 248 of these are positive commandments, and 365 are negative commandments. The well known ten commandments are among these 613.
Many of them are currently not possible to perform, as they involve doing things in the Temple. For example, there is a positive commandment to allow the Cohen eat the residue of the Meal Offerings in the Temple. As we don't have a Temple, we can't do this!
But a large number can be performed, and are every day.
The exact composition of the 613 varies slightly between authorities, but the most commonly used list is the Rambam's Sefer HaMitzvot. All 613 are either directly specified in the Torah, or are derived from things in the Torah.
613 may seem like a lot of things, and in many ways there's actually even more than 613 as each commandment may have various things that you need to do to keep it. But on the other hand, many things (such as Shabbat) are represented in many different commandments, concerned with different aspects of the practise.
Judaism has a lot of fun with numbers, as every Hebrew letter has a numeric value. This means that every Hebrew word also has a numeric value. One might think that the numeric value of "Torah" should be 613 - but in fact it's 611. The reason given is this.
When G-D was giving Moses the ten commandments and the other laws on Mount Sinai, at first he gave all the commandments in a "voice" loud enough for all the Children of Israel to hear. But after having heard the first two, they were so terrified to hear G-D's voice, the rest were given to Moses only, to be taught to the people. So the Torah was specifically needed for the remaining 611 commandments.