Algeria is a vast country with dramatically different climates from north to south, so the best time to visit depends entirely on where you are heading.
The coast and Tell Atlas (north). The Mediterranean strip around Algiers, Oran, and Bejaia has mild, wet winters and hot, dry summers. Spring (March to May) and autumn (September to November) are the most comfortable times to visit -- warm days, cool evenings, and manageable crowds. Summer is hot and humid along the coast, and cities empty out in August as everyone heads to the beach.
The Sahara. The desert is the main draw for many travelers, and timing matters enormously. Visit between October and March, when daytime temperatures are warm but bearable (20-30C) and nights are cool to cold. From May to September, the Sahara is punishingly hot -- 50C is not unusual in Adrar or In Salah. The best months for the Tassili n'Ajjer and Hoggar regions around Tamanrasset and Djanet are November to February.
The High Plateaux and Aures. The interior around Batna, Setif, and Constantine has a continental climate with cold winters (snow is common in the mountains) and hot summers. Spring and autumn are ideal for visiting the Roman ruins at Timgad and Djemila.
Ramadan affects travel significantly. Most restaurants close during daylight hours, and the pace of life changes. If you are not fasting, you will need to eat discreetly during the day. Evenings during Ramadan are lively and sociable, with streets and cafes coming alive after iftar. Ramadan follows the Islamic calendar and shifts forward roughly 11 days each year.
Festivals. The Sbou'a festival in Timimoun, celebrating the Prophet's birthday, is one of the most spectacular events in the Sahara. The annual festival in Tamanrasset brings together Tuareg music, culture, and camel races.