The country is at its best in summer, with long sunny days and short comfortable nights. The waters of the Baltic are actually warm enough to swim in (this might not be for everyone). Festivals erupt all over the country, including the spectacular 3-day Sea Festival of Klaipeda; the street life is vibrant and advance planning is required for hotels/activities.
The Baltic spring months are cool, with snowmelt feeding rivers, making it a great time for canoeing and other outdoor activities, but without the crowds. The autumn months of September November see an overshoot of peak-season tourists (but less so) because days are still sunny. This is also the time of classical music festivals and the famous Mama Jazz Festival in Vilnius.
As expected, the Baltic winters are cold and dark, with sub-zero temperatures and snow-covered landscapes. Expect continuous snowfall, ranging from light dust to heavy. Not much happening at this time; hotels and restaurants may be shut (except in the big cities), and it is not a pleasant time for a visit, overall.