At about 25 times faster than dial-up, 1.5 Mbps is a high-speed Internet connection, usually delivered over DSL. Whether or not it is sufficient depends entirely on your needs. With 1.5 Mbps of download speed, you should have no problem with basic Internet activity, but may find more bandwidth-intensive activity a bit sluggish. As with any Internet speed, running multiple Internet operations can slow your overall connection.
For the Internet basics like checking Facebook, reading the news, online shopping, checking email and instant messaging, 1.5Mbps is more than sufficient. Loading images and text should not present any problems, unless the page features a lot of large or animated images. Downloading large files will take longer on a 1.5Mbps connection, though not impossible.
1.5Mbps is right around the cusp for streaming video. Your connection shouldn't have issues with standard-quality video, but high-quality videos may stutter or lag on your connection. For instance, the VoIP service Skype recommends 4Mbps download speeds for the best video call quality, though it will work with a minimum of 512Kbps. Similarly, Amazon.com recommends a minimum of 1.5Mbps for their Video on Demand service, but suggests 3.5Mbps; Netflix requires 1.5Mbps for standard video, and 3Mbps for high quality.
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So long as you're not using other bandwidth-heavy activities, 1.5Mbps connections shouldn't have trouble streaming audio files, which are smaller and less complex than streaming video. Pandora, a well-known Internet radio service, requires a minimum 150Kbps for standard audio, and 300Kbps for high-quality content. Check with your streaming service regarding connection speeds if you're having trouble.
Game quality over your 1.5Mbps connection varies between games. For instance, the popular Blizzard game "World of Warcraft" doesn't list a connection speed requirement, instead simply stating that the game requires a broadband connection, and expanding that it is not suited for play on wireless or satellite Internet connections. Generally speaking, the more graphic data your game needs to load, the faster your connection requirements will be. If your game experiences lags or errors while playing, your Internet connection may not be up to the task.