Do you have to pay for Lord of the Rings Online to play

Lord of the Rings Online is free-to-play, so no you do not have to pay. There are things you can buy via the "LotRO Store" which are (for the most part) optional - the biggest and only memorable one is quest packs that give access to quests in regions. You can earn "Turbine Points" in-game that can be used to buy things in the store.
A Free-to-Play account has the following features.

• Play up to Level 75 (like even VIP accounts)
• Maximum of 2 characters per server. You can pick from any of the 4 races (Dwarf, Hobbit, Man, and Elf), and any of the 9 classes (Burglar, Captain, Champion, Guardian, Hunter, Lore-master, Minstrel).
• Questing available in Ered Luin, the Shire, and Bree and Lone-lands, as well as the full Epic Quest Line.
• You can enter all regions of the game with the exception of the Ettenmoors, which is the PvMP zone and therefore VIP.
• Legendary Item use at level 45.
• Up to Rank 7 for Skirmish Soldier traits.
• 2 virtue, race, and class traits and 1 legendary trait.
• Complete access to crafting through all seven tiers, and you can reach Acquaintance reputation standing with one crafting guild.

See the Related Links section for a complete list of all the account type features and such, and the more detailed list of all Free to Play account features.