If you are planning to travel with Shinkansen or express trains, it is better to reserve seats in advance to get a seat for sure. It tends to be crowded in morning and evening (business men for business trip) and weekends.
Especially during Golden Week (long holiday from end of April to early May), summer Obon holidays (roughly mid August), and new year holidays, tickets sell out fast.
Your question is a bit vague so it is important to clarify one big thing.
With the JR Pass, you don't need "tickets". You can ride any train the pass allows.
You are more likely referring to seat reservations. They are free with the pass. Given that, why not take advantage of something others have to pay for? You can also easily look up train schedules, routes and transfer info on Hyperdia.
However, if you really need seat reservations, generally speaking the answer is no. There are some very big travel periods like Golden Week, the end/start of the year and O-Bon when getting seat reservations would be very prudent. But most times seat availability is not an issue - most Japanese paying for tickets would opt for the Nozomi train which you cannot take with your pass. I've never had any problem getting a seat on an unreserved car, even during the cherry blossom season on shinkansen bound for Kyoto.
If you know your schedule and can stick to it, there is nothing wrong in making a seat reservation though. And if going to/from Kansai to Tokyo, you might want one like on the right hand side heading south or left hand side heading north - to be able to see some of Mt Fuji along the way (provided the weather cooperates, and it sometimes doesn't).
You can make the seat reservations in any JR office - so if you want to, do it.