Ultrasonic machines like the Sharper Image are a great idea, however, be careful! If your ring has colored stones, for example rubies - which are softer than diamonds, it can damage them! Also if you have a lot of delicate pave work in your ring, ultrasonic machines have been known to cause stones to fall out. However, ultrasonic machines give the best clean for all other types of rings.
Personally, I just soak my jewelry in jewelry cleaner solution and polish them with a jewelry cloth. You can get Connoisseurs (sp?) brand at any Walmart-type store, or get a house brand from your jewelry store. Some people find that diluted ammonia or diluted Windex also shines diamonds.